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A square is inscribed in a circle. The radius of the circle is $\frac{20\sqrt{2}}{2}$ inches. What is the side length, in inches, of the square?

MathGeometry and Trigonometry

The length of a rectangle's diagonal is $5\sqrt{17}$, and the length of the rectangle's shorter side is 5. What is the length of the rectangle's longer side?

MathGeometry and Trigonometry

What is the area of a rectangle with a length of 17 centimeters (cm) and a width of 7 cm?

MathGeometry and Trigonometry

The area of a rectangle is 630 square inches. The length of the rectangle is 70 inches. What is the width, in inches, of this rectangle?

MathGeometry and Trigonometry

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

MathGeometry and Trigonometry

Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is $\bm{K}$ $cm$${}^{2}$. If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}\bm{K}$ $cm$${}^{2}$. What is the side length, in cm, of each square base?

MathGeometry and Trigonometry

The equation $\bm{x}^{2}+\left(y-2\right)^{2}=36$ represents circle

MathGeometry and Trigonometry

$(x-6)^{2}+(y+5)^{2}=16$<br/><br/>In the $xy$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point $Q$ ?

MathGeometry and Trigonometry

What is the area, in square centimeters, of a rectangle with a length of 36 centimeters and a width of 34 centimeters?

MathGeometry and Trigonometry

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MathGeometry and Trigonometry

Triangles _ABC_ and _DEF_ are congruent, where $A$ corresponds to $D$, and $B$ and $E$ are right angles. The measure of angle $A$ is $18^{*}$. What is the measure of angle _F_?

MathGeometry and Trigonometry

In the $xy$-plane, a circle with radius 5 has center ($-8$,$6$). Which of the following is an equation of the circle?<br/><br/>$$

MathGeometry and Trigonometry

A circle has center $O$, and points $A$ and $B$ lie on the circle. The measure of arc $AB$ is $45^{\circ}$ and the length of arc $AB$ is 3 inches. What is the circumference, in inches, of the circle?

MathGeometry and Trigonometry

The equation $x^{2}+\left(y-1\right)^{2}=49$ represents circle

MathGeometry and Trigonometry

Triangle $ABC$ is similar to triangle $DEF$, where $A$ corresponds to $D$ and $C$ corresponds to $F$. Angles $C$ and $F$ are right angles. If $\tan(A)=\sqrt{3}$ and $DF=125$, what is the length of $\overline{DE}$?

MathGeometry and Trigonometry

The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

MathGeometry and Trigonometry

In triangle $ABC$, the measure of angle $B$ is $52^{\,*}$ and the measure of angle $C$ is $17^{\,*}$. What is the measure of angle $A$?

MathGeometry and Trigonometry

A right triangle has legs with lengths of 28 centimeters and 20 centimeters. What is the length of this triangle's hypotenuse, in centimeters?

MathGeometry and Trigonometry

A rectangle has a length of 13 and a width of 6. What is the perimeter of the rectangle?

MathGeometry and Trigonometry

$RS=20$<br/><br/>$ST=48$<br/><br/>$TR=52$<br/><br/>The side lengths of right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$.<br/>What is the value of $tan\ W$?

MathGeometry and Trigonometry

A right circular cone has a volume of $\frac{1}{3}$...

MathGeometry and Trigonometry

$RS=440$<br/><br/>$ST=384$<br/><br/>$TR=584$ $<br/><br/>The side lengths of right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$ . What is the value of $\tan W$?

MathGeometry and Trigonometry

An isosceles right triangle has a perimeter of $94+94\sqrt{2}$ inches. What is the length, in inches, of one leg of this triangle?

MathGeometry and Trigonometry

In the $xy$-plane, the graph of $2x^{2}-6x+2y^{2}+2y=45$ is a circle. What is the radius of the circle?

MathGeometry and Trigonometry

Triangle $ABC$ and triangle $DEF$ are similar triangles, where $AB$ and $DE$ are corresponding sides. If $DE=2AB$ and the perimeter of triangle $ABC$ is $20$, what is the perimeter of triangle $DEF$ ?

MathGeometry and Trigonometry