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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

Circumcircle of Squares

In the above diagram, square $ABCD$ is inscribed in circle $O,$ which is in turn inscribed in square $A'B'C'D'.$ If the length of $\overline{A'D'}$ is $\lvert\overline{A'D'}\rvert=8,$ what is $\lvert\overline{AD}\rvert?$

4(\sqrt{2}-1)

4

8(\sqrt{2}-1)

4\sqrt{2}

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by Brilliant Staff

The area of the square inscribed in circle $O$ in the above diagram is $484.$ What is the area of the shaded region?

363\pi-484

242\pi-484

484\pi-484

605\pi-484

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by Brilliant Staff

The area of the circle in the above diagram is $64\pi.$ What is the area of the inscribed square $ABCD?$

64 32 128 192

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In the above diagram, $\square ABCD$ is a square inscribed in circle $O,$ and $\overline{ON}$ is perpendicular to $\overline{BC}.$ If the length of $\overline{MN}$ is $2\sqrt{2}-2,$ what is the length of $\overline{BM}?$

2 6 1 4

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For which of the following quadrilaterals does a circumscribing circle always exist?

Square Rhombus Parallelogram Trapezoid

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by Brilliant Staff

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