All Questions ⁺⁰235750 Questions

0

11

1

+1246

Perimeter

The perimeter of the triangle below is an integer. What is the smallest possible value of the perimeter? (Assume that the triangle is non-degenerate.) read more ..

Akhain1 Mar 25, 2024

0

22

0

+359

Square

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

falafronk Mar 25, 2024

0

23

2

+359

Square

A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square.

falafronk Mar 25, 2024

0

30

0

+359

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

falafronk Mar 25, 2024

0

21

0

+359

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

falafronk Mar 25, 2024

+1

26

2

+1246

counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

Akhain1 Mar 25, 2024

+1

25

1

+359

Geometry

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

falafronk Mar 25, 2024

+1

34

0

+359

Triangle

In triangle ABC, point X is on side BC such that AX = 10, BC = 10, CX = 5, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.

falafronk Mar 25, 2024

+1

15

1

+704

Triangle

Find the circumradius of triangle $ABC.$

booboo44 Mar 25, 2024

+1

28

5

+14

help me out!!

Write as a product of two monic quadratics with integer coefficients.

●●●●●

svphxxo Mar 25, 2024

-1

21

1

+704

Triangle

Find the inradius of triangle ABC.

booboo44 Mar 25, 2024

-1

31

0

+359

Circle

A circle lies inside a quarter-circle, as shown below. The circle is tangent to side $\overline{AO}$ and arc $AB.$ Find the radius of the circle.

falafronk Mar 25, 2024

-1

25

0

+359

triangle

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

falafronk Mar 25, 2024

0

28

0

+1246

help counting

Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly five chi read more ..

Akhain1 Mar 25, 2024

-1

20

0

+359

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $BC = \sqrt{3}$, then find $AB$. read more ..

falafronk Mar 25, 2024

-1

24

0

+359

Circles

The two circles below are externally tangent. A common external tangent intersects line $PQ$ at $R.$ Find $QR.$

falafronk Mar 25, 2024

-1

30

0

+359

Circle

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius read more ..

falafronk Mar 25, 2024

-1

40

0

+359

help maximum

Let x and y be nonnegative real numbers. If x^2 + 3y^2 = 18, then find the maximum value of x + y.

falafronk Mar 25, 2024

0

19

1

+70

Find the area of triangle ABC, given that AH=11 and HD=5.

Find the area of triangle ABC, given that AH=11 and HD=5. read more ..

faiafronk Mar 25, 2024

0

27

1

+70

equilateral trianlge (last time was wrong)

Triangle DEF is equilateral. Find AE read more ..

faiafronk Mar 25, 2024

0

21

1

+70

geometry

In triangle ABC, point X is on side BC such that AX = 13, BC = 10, CX = 4, and the circumcircles of traingles ABX and ACX have the same radius. Find the area of triangle ABC.
(no diagram)

faiafronk Mar 25, 2024

0

19

1

+70

help!

Semicircles are constructed on AB, AC,and BC. A circle is tangent to all three semicircles. Find the radius of the circle. read more ..

faiafronk Mar 25, 2024

-1

21

0

+359

Minimum

Let x and y be nonnegative real numbers. If xy = \frac{2}{5}, then find the minimum value of 6x + \frac{3}{5y}.

falafronk Mar 25, 2024

-1

23

1

+359

Temperature

The temperature of a point (x,y) in the plane is given by the expression x^2 + y^2 - 4x + 2y - 12x + 14y + 26. What is the temperature of the coldest point in the plane?

falafronk Mar 25, 2024

-1

23

1

+359

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BZ$.

falafronk Mar 25, 2024

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