Problem

Source: Problem 1 Geometry

Tags: geometry, geometric transformation, reflection, trigonometry, perpendicular bisector, geometry unsolved



1-Let $ \triangle ABC$ be a triangle and $ (O)$ its circumcircle. $ D$ is the midpoint of arc $ BC$ which doesn't contain $ A$. We draw a circle $ W$ that is tangent internally to $ (O)$ at $ D$ and tangent to $ BC$.We draw the tangent $ AT$ from $ A$ to circle $ W$.$ P$ is taken on $ AB$ such that $ AP = AT$.$ P$ and $ T$ are at the same side wrt $ A$.PROVE $ \angle APD = 90^\circ$.