Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.2 Junior Find the answer

In the accompanying figure $\overline{CE}$ and $\overline{DE}$ are equal chords of a circle with center $O$ . Arc $AB$ is a quarter-circle. Then the ratio of the area of triangle $CED$ to the area of triangle $AOB$ is:

Pick one

Solution

Draw $OE$ . Since triangles $AOB$ , $COE$ , and $DOE$ are congruent, you can fit triangle $AOE$ twice in $CED$ . Thus, our answer is $(E)2:1$ .
$\fbox{}$

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