All Questions ⁺⁰236416 Questions

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+703

Geometry

A square is divided into five rectangles, and all the rectangles have the same area. Given that $AB = 1,$ find the side length of the square.

siIviajendeukie Jan 4, 2025

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1

+703

Geometry

Let WXYZ be a square. Let P be a point inside the square, so that triangle PWX is right isosceles. Compute \angle PYZ.

siIviajendeukie Jan 4, 2025

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1

+6

Anna would like to surround a photograph

Anna would like to surround an \[8\, \text{in}\times10\, \text{in}\] photograph with a border of uniform width. Let \[x\] be the width of the border, in inches. Which of the following functions could she use to determine the area, \[A\], read more ..

Starwarsguy Jan 4, 2025

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1

+553

Geometry

Chords \overline{PQ} and \overline{RS} of a circle meet at $X$ inside the circle. If $RS = 38$, $PX = 38$, and $QX = 36$, then what is the smallest possible value of $RX$?

crimefightingvigiI Jan 4, 2025

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3

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+553

Geometry

Circle O has radius 5. Segment $\overline{AS}$ has length $5$ and is tangent to circle $O$ at $A$. If $P$ is the projection of A onto OS, find length PS.

crimefightingvigiI Jan 4, 2025

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+553

Geometry

In a circle, \overline{AP} is a diameter of length 17 and $\overline{PS}$ is a chord of length 17. What is the length of chord $\overline{AS}$?

crimefightingvigiI Jan 4, 2025

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4

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+553

Geometry

Let A_1 A_2 A_3 \dotsb A_{12} be a regular polygon. If the area of A_1 A_2 A_3 \dotsb A_{12} is 1, then find the area of the blue region.

crimefightingvigiI Jan 4, 2025

Jan 3, 2025

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+178

Geometry

Two angle bisectors of triangle ABC, $\overline {BE}$ and $\overline {CF}$, intersect at $P$. What is $\angle A$ in degrees?

cwimie Jan 3, 2025

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+178

Geometry

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

cwimie Jan 3, 2025

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3

0

+178

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and $\overline{AD}$ bisects $\angle BDE.$ If $\angle CBD = 30^\circ$ and $\angle CED = 60^\circ,$ then find $\angle CAD,$ in degrees.

cwimie Jan 3, 2025

0

4

0

+178

Geometry

Triangle ABC is congruent to triangle DEF, but triangle ABC is not congruent to triangle XYZ. Which of the following relationships cannot hold?
ABC and DEF have the same area
ABC and DEF have the same perimeter
ABC read more ..

cwimie Jan 3, 2025

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1

+16

Help plzzzzz

For how many three-element sets (order doesn't matter) of positive integers is it true that ? (The positive integers and are distinct.)

adook101 Jan 3, 2025

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+697

Geometry

What is the measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio 4:2:8?

cooIcooIcooI17 Jan 3, 2025

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1

2

+402

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 $AB.$

MEMEG0D Jan 3, 2025

Jan 2, 2025

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1

1

+402

Geometry

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

MEMEG0D Jan 2, 2025

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+402

Geometry

Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?

MEMEG0D Jan 2, 2025

0

1

1

+402

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.

MEMEG0D Jan 2, 2025

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