Inscribed trapezoids problem

angleeuclidean-geometry

Let $ABCD$ be inscribed trapezoid with $(AB) \parallel (CD)$ and let $P$ be the point where its diagonals meet.

The circumcircle of $\triangle APB$ meets line $(BC)$ (again) at $X$.

$Y$ is a point on $(AX)$ such that $(DY)\parallel (BC)$.

Prove that $\angle YDA = 2 \angle YCA $.

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Any hints would be appreciated.

Best Answer

Some hints:

  • Prove that $ADPY$ is cyclic.

  • Prove that $PC=PY$.

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