All Questions

0

24

2

+1837

Geometry

Let XYZ be a triangle, and let XP, XQ, XR be the altitude, angle bisector, and median from X, respectively. If angle YQZ = 90^\circ and angle ZQX = 22^\circ, then what is the measure of angle RZP in degrees?

●●

blackpanther Dec 18, 2025

0

24

1

+1837

Geometry

Find the side length of the equilateral triangle.
AB = 1, CP = 4, PQ = 5, DA = 3, EP = 2

●

blackpanther Dec 18, 2025

0

24

1

+1837

Geometry

In the diagram, ABCD is a square with side length 2, and BEF is an equilateral triangle with side length 3. Find DF.

●

blackpanther Dec 18, 2025

0

24

2

+1837

Geometry

In the diagram, ABCD and AEFG are squares with side length 1. Find the area of the green region.

●●

blackpanther Dec 18, 2025

0

24

1

+202

Geometry

Shown below is rectangle $EFGH$. Its diagonals meet at $Y$. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If $FY = 24$ and $HX = 28$ and $EF = 10$, find the perimeter of rectangle $EFGH$.

●

HumanBemg Dec 18, 2025

0

24

1

+202

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and \overline{CE} bisects \angle ACD. Compute \angle BAC, in degrees.

●

HumanBemg Dec 18, 2025

0

24

1

+202

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and \overline{AD} bisects \angle CDA. If \angle CBD = 37^\circ and \angle CED = \angle ABC + 33^\circ, then find \angle BED, in degrees.

●

HumanBemg Dec 18, 2025

0

24

1

+1317

Geometry

ABCD is a square. Find AM.

●

AnswerscorrectIy Dec 18, 2025

0

24

1

+1317

Geometry

Trapezoid ABCD has bases AB and CD. Line segment EF, which is parallel to the bases, divides trapezoid ABCD into two trapezoids of equal perimeter. If AM = 10, and BN = 5, find the length EF.

●

AnswerscorrectIy Dec 18, 2025

0

23

1

+1317

Geometry

Find angle x, in degrees.
the angles of a triangle are x, 80, and 88.
Note: We say that a line bisects an angle if it splits it into two equal parts.

●

AnswerscorrectIy Dec 18, 2025

0

23

1

+1317

Geometry

FInd the value of x
Triangle with angles 50, 75, x

●

AnswerscorrectIy Dec 18, 2025

0

24

1

+33

Geometry

In the diagram, AD bisects BAC.
By adding one more condition, we can prove that triangles ABD and ACD are congruent. Which one of the following could be that condition? Select all that apply.
(a) BC read more ..

●

co1inqiu Dec 18, 2025

0

24

1

+33

Geometry

Select the two triangles that must be congruent.
ABC
DEF
GHI read more ..

●

co1inqiu Dec 18, 2025

0

24

1

+33

Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

●

co1inqiu Dec 18, 2025

0

24

1

+125

Geometry

Triangles RST and XYZ are congruent. Point P lies on ST, and point W lies on XY. Select all the true statements.
(a) If RST is isosceles, then XYZ is isosceles.
(b) If ST = 6, then WY = 6
(c) If RP \perp ST, read more ..

●

BlackoutMiIkshake Dec 18, 2025

0

24

1

+125

Geometry

A straight line \ell divides a triangle \Delta into two congruent triangles. Select all the statements that must be true.
(a) If Delta is isoceles, then it is equilateral
(b) If Delta is right, then it is equilateral
(c) read more ..

●

BlackoutMiIkshake Dec 18, 2025

0

24

1

+125

Geometry

Find AE
BE = 30, PE = 18, CP = 10

●

BlackoutMiIkshake Dec 18, 2025

0

24

1

+125

Geometry

In triangle ABC, AB = AC. Find angle BAC in degrees.
AD = 5
DE = 7
BE = 3 read more ..

●

BlackoutMiIkshake Dec 18, 2025

0

24

1

+507

Geometry

The centroid of triangle ABC is G. Find x, in degrees.

●

bIueb3rry Dec 17, 2025

0

24

1

+507

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

●

bIueb3rry Dec 17, 2025

0

24

1

+1011

Geometry

In triangle ABC, M is the midpoint of \overline{BC}, E is the midpoint of \overline{AB}, and D is the midpoint of \overline{AM}. Point T is the intersection of \overline{BD} and \overline{ME}. Find the area of triangle XYZ if [ABC] = 14. read more ..

●

gnistory Dec 17, 2025

0

24

1

+1011

Geometry

In triangle ABC, the orthocenter H lies on altitude \overline{AD}. Find \frac{AH}{HD}.

●

gnistory Dec 17, 2025

0

24

1

+1011

Geometry

The centroid of triangle ABC is G. Find BG.

●

gnistory Dec 17, 2025

0

24

1

+1011

Geometry

In triangle ABC, \angle A = 90^\circ. Altitude $\overline{AP},$ angle bisector $\overline{AQ},$ and median $\overline{AR}$ are drawn. If $PQ = 3$ and $QC = 4,$ find $AR.$

●

gnistory Dec 17, 2025

0

23

1

+616

Geometry

The incircle of triangle ABC is shown. Find x, in degrees.

●

onyuIee Dec 17, 2025

0

1

+616

Geometry

Find the area of triangle ABC if AH=6, AQ=4, and CQ=11 in the diagram below.

●

onyuIee Dec 17, 2025

0

1

+322

Geometry

If ST = 2, QS = 4, and PT = 5, find PQ.

●

CInsbstnkng Dec 17, 2025

0

1

+322

Geometry

In rectangle ABCD, corner A is folded over crease DE to point F on BC. Find BC.

●

CInsbstnkng Dec 17, 2025

+1

1

2

+5

Please help me

On a number line, C is twice as far from A as it is from B if the lenth of AB = 7.5 inches, find the number of inches between the 2 possible locations for C?

●●

Omer8thgrade Dec 17, 2025

+1

1

+314

Number Theory

For a positive integer n, let \tau(n) be the sum of the positive integer divisors of n. Find the number of values of n, where 1 \le n \le 25, such that \tau(n) = 1.

●

AUnVerifedTaxPayer Dec 16, 2025

+1

1

+314

Geometry

I is the incenter of triangle ABC. Find DE.

●

AUnVerifedTaxPayer Dec 16, 2025

+1

1

2

+314

Geometry

Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

●●

AUnVerifedTaxPayer Dec 16, 2025

+1

1

+314

Geometry

Triangle ABC has circumcenter O. What is \angle AOC, in degrees?

●

AUnVerifedTaxPayer Dec 16, 2025

+1

1

+12

The Perfect Square of Balanced Binary Matrices

Let S be the set of 2n \times 2n matrices whose entries are 0 or 1. A matrix M \in S is called good if in every row and every column, the sum of the entries is exactly n.
Prove that the number of good matrices is a perfect square.

●

kotonarski Dec 16, 2025

+1

1

+12

The Riemann Hypothesis Challenge

💥 The Ultimate Mathematical Challenge
The problem is to prove the Riemann Hypothesis (RH), a conjecture about the non-trivial zeros of the analytic continuation of the Riemann Zeta Function, \zeta(s).
The Equation and The Function read more ..

●

kotonarski Dec 16, 2025

0

1

2

+1837

Geometry

Let XYZ be a triangle, and let XP, XQ, XR be the altitude, angle bisector, and median from X, respectively. If angle YQZ = 90^\circ and angle ZQX = 22^\circ, then what is the measure of angle RZP in degrees?

●●

blackpanther Dec 15, 2025

-1

1

+1837

Geometry

Find the side length of the equilateral triangle.
AB = 1, CP = 4, PQ = 5, DA = 3, EP = 2

●

blackpanther Dec 15, 2025

-1

1

2

+1837

Geometry

In the diagram, ABCD is a square with side length 2, and BEF is an equilateral triangle with side length 3. Find DF.

●●

blackpanther Dec 15, 2025

-1

1

+1837

Geometry

In the diagram, ABCD and AEFG are squares with side length 1. Find the area of the green region.

●

blackpanther Dec 15, 2025

0

1

+4

Algabra

Graph the inequality on the axes below.
y, is greater than, minus, start fraction, 5, divided by, 6, end fraction, x, minus, 5
y>−65x−5

●

Isukathw Dec 15, 2025

0

2

+869

Geometry

Shown below is rectangle $EFGH$. Its diagonals meet at $Y$. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If $FY = 24$ and $HX = 28$ and $EF = 10$, find the perimeter of rectangle $EFGH$.

●●

cooIcooIcooI17 Dec 12, 2025

0

1

+869

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and \overline{CE} bisects \angle ACD. Compute \angle BAC, in degrees.

●

cooIcooIcooI17 Dec 12, 2025

0

1

+869

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and \overline{AD} bisects \angle CDA. If \angle CBD = 37^\circ and \angle CED = \angle ABC + 33^\circ, then find \angle BED, in degrees.

●

cooIcooIcooI17 Dec 12, 2025

+1

1

+1011

Geometry

ABCD is a square. Find AM.

●

gnistory Dec 12, 2025

0

1

+1011

Geometry

Trapezoid ABCD has bases AB and CD. Line segment EF, which is parallel to the bases, divides trapezoid ABCD into two trapezoids of equal perimeter. If AM = 10, and BN = 5, find the length EF.

●

gnistory Dec 12, 2025

0

1

2

+1011

Geometry

Find angle x, in degrees.
the angles of a triangle are x, 80, and 88.
Note: We say that a line bisects an angle if it splits it into two equal parts.

●●

gnistory Dec 12, 2025

0

1

2

+1011

Geometry

FInd the value of x
Triangle with angles 50, 75, x

●●

gnistory Dec 12, 2025

0

1

+1011

Geometry

Select the two triangles that must be congruent.
ABC
DEF
GHI read more ..

●

gnistory Dec 12, 2025

0

1

+1011

Geometry

In the diagram, AD bisects BAC.
By adding one more condition, we can prove that triangles ABD and ACD are congruent. Which one of the following could be that condition? Select all that apply.
(a) BC read more ..

●

gnistory Dec 12, 2025

0

1

+16

Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

●

illrelyt Dec 12, 2025

0

1

+16

Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

●

illrelyt Dec 12, 2025

0

1

+16

Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

●

illrelyt Dec 12, 2025

0

1

+16

Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

●

illrelyt Dec 12, 2025

0

1

+1572

Geometry

Triangles RST and XYZ are congruent. Point P lies on ST, and point W lies on XY. Select all the true statements.
(a) If RST is isosceles, then XYZ is isosceles.
(b) If ST = 6, then WY = 6
(c) If RP \perp ST, read more ..

●

kittykat Dec 12, 2025

0

1

+1572

Geometry

A straight line \ell divides a triangle \Delta into two congruent triangles. Select all the statements that must be true.
(a) If Delta is isoceles, then it is equilateral
(b) If Delta is right, then it is equilateral
(c) read more ..

●

kittykat Dec 12, 2025

0

1

+1572

Geometry

Find AE
BE = 30, PE = 18, CP = 10

●

kittykat Dec 12, 2025

0

1

+1572

Geometry

In triangle ABC, AB = AC. Find angle BAC in degrees.
AD = 5
DE = 7
BE = 3 read more ..

●

kittykat Dec 12, 2025

0

1

+359

Geometry

In rectangle ABCD, \frac{[AEP]}{[DFP]} = 5. Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

●

jaekg Dec 12, 2025

0

1

+359

Geometry

In the diagram, ABCD is a rectangle, and BEFG is a square. Find AD.

●

jaekg Dec 12, 2025

0

1

+359

Geometry

Which of the following conditions ensures that triangles ABC and DEF are similar? Select all that apply.
(1) A = B, D = C, F = E, B = A, AB/AD = BC/BE
(2) A = D, AB/EF = BC/DE
(3) AB perp CD, DE perp AE, AB = DE read more ..

●

jaekg Dec 12, 2025

0

1

+359

Geometry

Find the perimeter of triangle XYZ.
YZ = 10, YP = 6, XQ = 4, XP = 8, PQ = 7

●

jaekg Dec 12, 2025

0

1

+507

Geometry

In the diagram, AB is parallel to CD. Select the two products of lengths that must be equal.
AO \cdot BO
BO \cdot CE
CO \cdot AB read more ..

●

bIueb3rry Dec 12, 2025

0

1

+507

Geometry

Find length BC
AB = 13, AP = 12, BAC = 2*BPC, AC \perp BD

●

bIueb3rry Dec 12, 2025

0

1

+507

Geometry

If ST = 2, QS = 4, and PT = 5, find PQ.

●

bIueb3rry Dec 12, 2025

0

1

+507

Geometry

In rectangle ABCD, corner A is folded over crease DE to point F on BC. Find BC.

●

bIueb3rry Dec 12, 2025

0

1

+7

Im stuck on this. can u help

There are 3 red balls and 2 blue balls. A ball is randomly selected one at a time without replacement until a red ball is selected.Find the probability that it takes 3 times to select a red ball.

●

ilrelyt Dec 12, 2025

0

1

+322

Geometry

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at P. If [APD]=3 and [BAD]=8, then what is [PAB]?

●

CInsbstnkng Dec 11, 2025

-1

1

3

+322

Geometry

ABCD is a parallelogram. Find DG.

●●●

CInsbstnkng Dec 8, 2025

0

1

+322

Geometry

In trapezoid PQRS, Base PQ is parallel to base RS. Let point X be the intersection of diagonals PR and QS. The area of triangle PQR is 4 and the area of triangle QRX is 4. Find the area of trapezoid PQRS

●

CInsbstnkng Dec 8, 2025

0

1

+322

Geometry

In trapezoid ABCD, \overline{AB} \parallel \overline{CD}. Find the area of the trapezoid.

●

CInsbstnkng Dec 8, 2025

0

1

+322

Geometry

Let WXYZ be a trapezoid with bases \overline{XY} and \overline{WZ}. In this trapezoid, \angle XWZ = 81, angle WXY = 62, and angle ZYW = 137. Find \angle YWZ, in degrees.

●

CInsbstnkng Dec 8, 2025

-1

1

2

+869

Geometry

The centroid of triangle ABC is G. Find x, in degrees.

●●

cooIcooIcooI17 Dec 5, 2025

0

1

+869

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

●

cooIcooIcooI17 Dec 5, 2025

0

1

+987

Geometry

In triangle ABC, M is the midpoint of \overline{BC}, E is the midpoint of \overline{AB}, and D is the midpoint of \overline{AM}. Point T is the intersection of \overline{BD} and \overline{ME}. Find the area of triangle XYZ if [ABC] = read more ..

●

booboo44 Dec 5, 2025

0

1

+987

Geometry

In triangle ABC, the orthocenter H lies on altitude \overline{AD}. Find \frac{AH}{HD}.

●

booboo44 Dec 5, 2025

0

1

+987

Geometry

The centroid of triangle ABC is G. Find BG.

●

booboo44 Dec 5, 2025

0

1

+987

Geometry

In triangle ABC, \angle A = 90^\circ. Altitude $\overline{AP},$ angle bisector $\overline{AQ},$ and median $\overline{AR}$ are drawn. If $PQ = 3$ and $QC = 4,$ find $AR.$

●

booboo44 Dec 5, 2025

0

1

+987

Geometry

The incircle of triangle ABC is shown. Find x, in degrees.

●

booboo44 Dec 5, 2025

0

1

+987

Geometry

Find the area of triangle ABC if AH=6, AQ=4, and CQ=11 in the diagram below.

●

booboo44 Dec 5, 2025

0

2

+224

Geometry

I is the incenter of triangle ABC. Find DE.

●●

BRAlNBOLT Dec 3, 2025

0

1

2

+224

Geometry

Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

●●

BRAlNBOLT Dec 3, 2025

0

1

2

+322

Geometry

Triangle ABC has circumcenter O. What is \angle AOC, in degrees?

●●

CInsbstnkng Dec 3, 2025

0

1

+322

Geometry

Let XYZ be a triangle, and let XP, XQ, XR be the altitude, angle bisector, and median from X, respectively. If angle YQZ = 90^\circ and angle ZQX = 22^\circ, then what is the measure of angle RZP in degrees?

●

CInsbstnkng Dec 2, 2025

0

2

1

+322

Geometry

Find the side length of the equilateral triangle.
AB = 1, CP = 4, PQ = 5, DA = 3, EP = 2

●

CInsbstnkng Dec 2, 2025

0

1

+322

Geometry

In the diagram, ABCD is a square with side length 2, and BEF is an equilateral triangle with side length 3. Find DF.

●

CInsbstnkng Dec 2, 2025

0

1

+322

Geometry

In the diagram, ABCD and AEFG are squares with side length 1. Find the area of the green region.

●

CInsbstnkng Dec 2, 2025

0

1

2

+322

Geometry

In rectangle ABCD, corner A is folded over crease DE to point F on BC. Find BC.

●●

CInsbstnkng Dec 2, 2025

0

1

+322

Geometry

If ST = 2, QS = 4, and PT = 5, find PQ.

●

CInsbstnkng Dec 2, 2025

0

1

+1317

Geometry

Find length BC
AB = 13, AP = 12, BAC = 2*BPC, AC \perp BD

●

AnswerscorrectIy Dec 1, 2025

0

1

+1317

Geometry

In the diagram, AB is parallel to CD. Select the two products of lengths that must be equal.
AO \cdot BO
BO \cdot CE
CO \cdot AB read more ..

●

AnswerscorrectIy Dec 1, 2025

0

1

2

+1317

Geometry

Find the perimeter of triangle XYZ.
YZ = 10, YP = 6, XQ = 4, XP = 8, PQ = 7

●●

AnswerscorrectIy Dec 1, 2025

0

1

2

+1317

Geometry

Which of the following conditions ensures that triangles ABC and DEF are similar? Select all that apply.
(1) A = B, D = C, F = E, B = A, AB/AD = BC/BE
(2) A = D, AB/EF = BC/DE
(3) AB perp CD, DE perp AE, AB = DE read more ..

●●

AnswerscorrectIy Dec 1, 2025

0

1

2

+987

Geometry

In the diagram, ABCD is a rectangle, and BEFG is a square. Find AD.

●●

booboo44 Nov 27, 2025

0

1

+987

Geometry

In rectangle ABCD, \frac{[AEP]}{[DFP]} = 5. Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

●

booboo44 Nov 27, 2025

0

1

+987

Geometry

In triangle ABC, AB = AC. Find angle BAC in degrees.
AD = 5
DE = 7
BE = 3 read more ..

●

booboo44 Nov 27, 2025

0

1

+987

Geometry

Find AE
BE = 30, PE = 18, CP = 10

●

booboo44 Nov 26, 2025

0

1

+987

Geometry

A straight line \ell divides a triangle \Delta into two congruent triangles. Select all the statements that must be true.
(a) If Delta is isoceles, then it is equilateral
(b) If Delta is right, then it is equilateral
(c) read more ..

●

booboo44 Nov 26, 2025

0

1

+1761

Geometry

Triangles RST and XYZ are congruent. Point P lies on ST, and point W lies on XY. Select all the true statements.
(a) If RST is isosceles, then XYZ is isosceles.
(b) If ST = 6, then WY = 6
(c) If RP \perp ST, read more ..

●

parmen Nov 26, 2025

0

1

+1761

Geometry

In the diagram, AD bisects BAC.
By adding one more condition, we can prove that triangles ABD and ACD are congruent. Which one of the following could be that condition? Select all that apply.
(a) BC read more ..

●

parmen Nov 26, 2025

0

1

+1761

Geometry

Select the two triangles that must be congruent.
ABC
DEF
GHI read more ..

●

parmen Nov 26, 2025

0

1

3

+1761

Geometry

FInd the value of x
Triangle with angles 50, 75, x

●●●

parmen Nov 26, 2025

0

1

2

+1761

Geometry

Find angle x, in degrees.
the angles of a triangle are x, 80, and 88.
Note: We say that a line bisects an angle if it splits it into two equal parts.

●●

parmen Nov 26, 2025

0

1

+1761

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and \overline{AD} bisects \angle CDA. If \angle CBD = 37^\circ and \angle CED = \angle ABC + 33^\circ, then find \angle BED, in degrees.

●

parmen Nov 26, 2025

0

1

2

+1761

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and \overline{CE} bisects \angle ACD. Compute \angle BAC, in degrees.

●●

parmen Nov 26, 2025

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