Question 87
Let $ABC$ be a triangle with $\angle BAC \neq 45^{\circ}$ and $\angle ABC \neq 135^{\circ}$. Let $P$ be the point on the line $AB$ with $\angle CPB = 45^{\circ}$. Let $O_1$ and $O_2$ be the circumcenters of the triangles $ACP$ and $BCP$. Show that the area of the quadrilateral $CO_1PO_2$ is equal to the area of the triangle $ABC$.