Question 61
Let $ABC$ be a right triangle with hypotenuse $AB$ and $P$ be a point inside the shorter arc $AC$ of the circumcircle of the triangle $ABC$. The line perpendicular to $CP$ which passes through $C$ intersects the lines $AP$ and $BP$ in points $K$ and $L$ respectively. Prove that the ratio of the areas of the triangles $BKL$ and $ACP$ does not depend on the choice of the point $P$.