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UKMT Mathematical Olympiad for Girls, 2021

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows a quadrilateral $ABCD$ , where $AB$ is $2$ cm and $\angle ABC$ , $\angle ACD$ and $\angle DAB$ are right angles. Let $E$ be the point on $DA$ such that $CE$ is perpendicular to $DA$ . Prove that triangles $ABC$ and $DEC$ are similar.

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