All Questions ⁺⁰234526 Questions

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+1694

geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

ABJeIIy Jul 20, 2024

-1

7

1

+1694

Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

ABJeIIy Jul 20, 2024

-1

7

0

+1694

Geometry

In trapezoid EFGH, \overline{EF} \parallel \overline{GH}, and P is the point on \overline{EH} such that EP:PH = 1:2. If the area of triangle PEF is 6, and the area of triangle PGH is 6, then find the area of trapezoid EFGH.

ABJeIIy Jul 20, 2024

-1

11

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+1694

Geometry

Quadrilateral ABCD is a parallelogram. Let E be a point on \overline{AB}, and let F be the intersection of lines DE and BC. The area of triangle EBF is 1, and the area of triangle BCE is 2. Find the area of parallelogram ABCD.

ABJeIIy Jul 20, 2024

0

5

1

+273

Geometry

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point.
An equilateral triangle, a regular decagon, and a regular n-gon, all with the same side length, also completely surround a read more ..

ABJelly Jul 20, 2024

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7

0

+856

Geometry

In trapezoid PQRS, \overline{PQ} \parallel \overline{RS}. Let X be the intersection of diagonals \overline{PR} and \overline{QS}. The area of triangle PRS is 27, and the area of triangle PQR is 75. Find the area of trapezoid PQRS read more ..

Rangcr897 Jul 20, 2024

0

5

0

+856

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $AMC$ if $[ABC] = 14$. read more ..

Rangcr897 Jul 20, 2024

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4

0

+856

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 ..

Rangcr897 Jul 20, 2024

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3

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+9

There is a point $P$ inside equilateral $\triangle ABC$ such that $PA=PB=PC=x.$ We know $[ABC]=\dfrac{\sqrt 3}{3}.$ Find $x.$

There is a point $P$ inside equilateral $\triangle ABC$ such that $PA=PB=PC=x.$ We know $[ABC]=\dfrac{\sqrt 3}{3}.$ Find $x.$

sticknotes.com Jul 20, 2024

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7

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+1015

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$

learnmgcat Jul 20, 2024

0

9

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+1015

Geometry

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

learnmgcat Jul 20, 2024

0

1

0

+1015

Geometry

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

learnmgcat Jul 20, 2024

0

7

0

+1015

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

learnmgcat Jul 20, 2024

-1

5

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+1694

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

ABJeIIy Jul 20, 2024

-1

7

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+1694

Geometry

Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.
AB = 8, AC = 12, CB = 8

ABJeIIy Jul 20, 2024

-1

5

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+1694

Geometry

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

ABJeIIy Jul 20, 2024

-1

6

0

+1694

geometry

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

ABJeIIy Jul 20, 2024

Jul 19, 2024

+1

6

1

+273

Geometry

Let IJKLMN be a hexagon with side lengths IJ=IM=3, JK = MN = 4 and KL = NI = 6. Also, all the interior angles of the hexagon are equal. Find the area of hexagon .

ABJelly Jul 19, 2024

0

4

1

+2633

Algebra problem

Sophie's favorite (positive) number is a two-digit number. If she reverses the digits, the result is $18$ less than her favorite number. Also, one digit is $2$ less than double the other digit. What is Sophie's favorite number? read more ..

LiIIiam0216 Jul 19, 2024

0

2

1

+593

Plz help!

Help I'm having trouble with this:
Let's take a look at (x + y)^2 (x - y)^2 and (x^2 + y^2)(x^2 - y^2). While Beeker believes that these two expressions are equal for all real numbers x and y Clod believes they are not! Let's get read more ..

AnswerscorrectIy Jul 19, 2024

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