falafronk

94 Questions
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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.

falafronk Mar 31, 2024

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15

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Rectangle

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

falafronk Mar 27, 2024

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33

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+359

Parallelogram

Find the area of parallelogram ABCD.

falafronk Mar 27, 2024

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14

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Rhombus

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

falafronk Mar 27, 2024

0

23

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+359

help trapezoid

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

falafronk Mar 27, 2024

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25

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+359

Trapezoid

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

falafronk Mar 27, 2024

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35

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+359

Angles

A quadrilateral has angles of $q$, $4q + 17^\circ $, $8q + 21^\circ$, and $15q + 148^\circ $. Find the largest angle of the quadrilateral, in degrees.

falafronk Mar 27, 2024

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18

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Triangle

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

falafronk Mar 27, 2024

0

16

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+359

Triangle

All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are co read more ..

falafronk Mar 27, 2024

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9

2

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Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

falafronk Mar 27, 2024