PAGMO 2021 Problem 2

Consider the isosceles right triangle $ABC$ with $\angle BAC = 90^\circ$ . Let $\ell$ be the line passing through $B$ and the midpoint of side $AC$ . Let $\Gamma$ be the circumference with diameter $AB$ . The line $\ell$ and the circumference $\Gamma$ meet at point $P$ , different from $B$ . Show that the circumference passing through $A,\ C$ and $P$ is tangent to line $BC$ at $C$ .