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UKMT Maclaurin Olympiad, 2020

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows a triangle $ABC$ and two lines $AD$ and $BE$ , where $D$ is the midpoint of $BC$ and $E$ lies on $CA$ . The lines $AD$ and $BE$ meet at $Z$ , the midpoint of $AD$ .

What is the ratio of the length $CE$ to the length $EA$ ?

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