Problem

Source: Chinese TST 2009 4th P1

Tags: geometry, circumcircle, trigonometry, geometric transformation, reflection, trapezoid, symmetry



Given that points $ D,E$ lie on the sidelines $ AB,BC$ of triangle $ ABC$, respectively, point $ P$ is in interior of triangle $ ABC$ such that $ PE = PC$ and $ \bigtriangleup DEP\sim \bigtriangleup PCA.$ Prove that $ BP$ is tangent of the circumcircle of triangle $ PAD.$