All Questions ⁺⁰235735 Questions

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help with geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Akhain1 Mar 19, 2024

+1

16

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+1246

Semicircles

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

Akhain1 Mar 19, 2024

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+43

Geometry

Point P is on side AC of triangle ABC such that

NinvisibleYT Mar 19, 2024

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18

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+1246

Triangle

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

Akhain1 Mar 19, 2024

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Trapezoid

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

Akhain1 Mar 19, 2024

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24

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+16

Helppppp I can’t do geometry

Suppose triangle TIP and triangle TOP isosceles triangles. Also suppose that TI=5, PI=7 and PO=11.
What is the sum of all possible lengths for TP?

ChunkerPanda100 Mar 19, 2024

Mar 18, 2024

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15

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Circles

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

Akhain1 Mar 18, 2024

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need help

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 ..

Akhain1 Mar 18, 2024

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Altitudes

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

Akhain1 Mar 18, 2024

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36

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Triangle

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

Akhain1 Mar 18, 2024

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26

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+1246

help geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

Akhain1 Mar 18, 2024

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+1246

Triangle

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

Akhain1 Mar 18, 2024

0

25

1

+1246

help geometry

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

Akhain1 Mar 18, 2024

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geometry

Triangle $MNO$ is an isosceles triangle with $MN = NO = 25\;\text{cm}$. A line segment, drawn from the midpoint of $\overline{MO}$ perpendicular to $\overline{MN}$, intersects $\overline{MN}$ at point $P$ with $NP:PM = 2:1$. What is the length of the altitude read more ..

Akhain1 Mar 18, 2024

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Isosceles triangle

In isosceles triangle ABC, we have AB=AC=4. The altitude from B meets AC at H. If AH=2(HC) then determine BC.

Akhain1 Mar 18, 2024

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Coordinates

A rectangle with vertices A(0,0), B(5,0), C(5,3) and D(0,3) is graphed in a coordinate plane. The rectangular region determined by those points is rotated $360^\circ$ about the line $y=-2$, forming a geometric solid. The rectangular region is then rotated read more ..

Akhain1 Mar 18, 2024

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+1246

need help

In triangle ABC, point X is on AC such that angle BXA=90 degrees, AX=12 and CX=5 What is BX?

Akhain1 Mar 18, 2024

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31

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+1246

help geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

Akhain1 Mar 18, 2024

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32

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+85

Geometry

These questions are difficult
1.

2.
<#> 3.<#> read more ..

Akhaim1 Mar 18, 2024

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28

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+1246

Triangle

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.

Akhain1 Mar 18, 2024

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+1246

Geometry

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

Akhain1 Mar 18, 2024

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18

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+359

Median

In triangle $ABC$, $AB = 7$, $AC = 15$, and the length of median $AM$ is $7$. Find the area of triangle $ABC$.

falafronk Mar 18, 2024

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30

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+359

Rhombus

If the area of a rhombus is 20 square inches and one of its diagonals is 10 inches, what is the length, in inches, of the other diagonal?

falafronk Mar 18, 2024

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34

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+359

Trapezoid

In the trapezoid $ABCD$, $\overline{AB}$ is parallel to $\overline{CD}$, $AB = \frac{2}{5} CD$, and point $P$ lies on $\overline{AB}$. What is the ratio of the area of triangle $DPC$ to the area of trapezoid $ABCD$? Express your answer as a common frac read more ..

falafronk Mar 18, 2024

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23

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+359

Trapezoid

Given an isosceles trapezoid with bases of 8 and 18 and an area of 120 square units, what is the number of units in the length of one of the non-parallel sides?

falafronk Mar 18, 2024

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