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UKMT Senior Mathematical Challenge, 2018

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A square is inscribed in a circle of radius 1. An isosceles triangle is inscribed in the square as shown. What is the ratio of the area of this triangle to the area of the shaded region?

(A) $\pi:\sqrt{2}$ (B) $\pi:1$ (C) $1:4$ (D) $1:\pi-2$ (E) $2:\pi$

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