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Problem 278

Geometry Difficulty 2.2 Multiple choice CEMC Fermat · Canada · 2014

Square $WXYZ$ has area 9 and $W$ is at the centre of a circle.

If $X$ and $Z$ are on the circle, the area of the circle is

Pick one

Official solution

Since square $WXYZ$ has area 9, then its side length is $\sqrt{9} = 3$ .

Since $W$ is the centre of the circle and $X$ lies on the circumference of the circle, then $WX$ is a radius of the circle, so the radius of the circle has length 3.

Therefore, the area of the circle is $\pi(3^2)=9\pi$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.