Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 5.2 AIME, harder Find the answer

28. Circles $\Omega_{1}$ and $\Omega_{2}$ of equal radii intersect at points $B$ and $C$ . A point $A$ is chosen on circle $\Omega_{1}$ . Ray $A B$ intersects circle $\Omega_{2}$ at point $D$ (point $B$ lies between points $A$ and $D$ ). On ray $D C$ , a point $E$ is chosen such that $D C = C E$ . Find $A E$ , if param1.

param1	Answer
$A C=5, A D=6$
$A C=5, A D=8$
$A C=13, A D=10$
$A C=13, A D=24$

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

param1	Answer
$A C=5, A D=6$	8
$A C=5, A D=8$	6
$A C=13, A D=10$	24
$A C=13, A D=24$	10

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.