Question 18
In a convex quadrilateral $ABCD$ we have that:
* $R$ and $S$ are points in the interior of the segments $CD$ and $AB$ respectively, with $AD = CR$ and $BC = AS$.
* $P$ and $Q$ are the midpoints of $DR$ and $SB$ respectively.
* $M$ is the midpoint of $AC$.
If it is known that $\angle MPC + \angle MQA = 90^\circ$, prove that $ABCD$ is a cyclic quadrilateral.
* $R$ and $S$ are points in the interior of the segments $CD$ and $AB$ respectively, with $AD = CR$ and $BC = AS$.
* $P$ and $Q$ are the midpoints of $DR$ and $SB$ respectively.
* $M$ is the midpoint of $AC$.
If it is known that $\angle MPC + \angle MQA = 90^\circ$, prove that $ABCD$ is a cyclic quadrilateral.