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Geometry

Inscribed and Circumscribed Figures

Concept Quizzes

Circumcircle of Triangle
Incircle of Triangle
Circumcircle of Squares
Incircle of Squares

Challenge Quizzes

Inscribed and Circumscribed Figures: Level 2 Challenges
Inscribed and Circumscribed Figures: Level 3 Challenges
Inscribed and Circumscribed Figures: Level 4 Challenges
Inscribed and Circumscribed Figures: Level 5 Challenges

Incircle of Triangle

In the above diagram, $\triangle ABC$ is an equilateral triangle and point $O$ is the center of the circle inscribed in $\triangle ABC.$ If the length of $\overline{AB}$ is $\lvert \overline{AB} \rvert = 27,$ $\overline{AB} \text{ and } \overline{OD}$ are parallel, and $\overline{AC} \text{ and } \overline{OE}$ are parallel, what is $\lvert\overline{DE}\rvert(=x)?$

10 9 12 11

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by Brilliant Staff

In the above diagram, circle $O$ is the incircle of right triangle $ABC.$ Given the two side lengths $\lvert\overline{AB}\rvert = 7 \text{ and }\lvert\overline{BC}\rvert = 16,$ what is the area of the circle?

Note: The above diagram is not drawn to scale.

\frac{37632}{834+\sqrt{645380}}\pi

\frac{12544}{854+\sqrt{645380}}\pi

\frac{12544}{834+\sqrt{645480}}\pi

\frac{12544}{834+\sqrt{645380}}\pi

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by Brilliant Staff

In the above diagram, circle $O$ is inscribed in triangle $\triangle ABC,$ with points of contact $D, E,$ and $F$ . If $\angle DBE = 54^{\circ} \text{ and } \angle DAF = 46^{\circ},$ what is $\angle BOC?$

Note: The above diagram is not drawn to scale.

{108}^\circ

{113}^\circ

{118}^\circ

{123}^\circ

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by Brilliant Staff

In the above diagram, circle $O$ is inscribed in $\triangle ABC$ , with points of contact at points $D, E$ and $F$ . If $a=4, b=7$ and $c=9,$ what is the perimeter of triangle $\triangle ABC?$

Note: The above diagram is not drawn to scale.

42 44 40 38

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by Brilliant Staff

In the above diagram, circle $O$ with radius $r=20$ is inscribed in $\triangle ABC$ . If the perimeter of $\triangle ABC$ is $x$ and the area of $\triangle ABC$ is $y$ , what is $\frac{y}{x}?$

9 10 12 11

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by Brilliant Staff