Inscribed and Circumscribed Figures

Circumcircle of Squares


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

The area of the square inscribed in circle OO in the above diagram is 484.484. What is the area of the shaded region?

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

In the above diagram, ABCD\square ABCD is a square inscribed in circle O,O, and ON\overline{ON} is perpendicular to BC.\overline{BC}. If the length of MN\overline{MN} is 222,2\sqrt{2}-2, what is the length of BM?\overline{BM}?

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


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