Question 105
The diagonals $AC$ and $BD$ of a cyclic quadrilateral $ABCD$ intersect at $P$.
The circumcircle of the triangle $PDC$ intersects $BC$ and $AD$ at $E$ and $F$, respectively. The circumcircle of the triangle $PAB$ cuts $BC$ and $AD$ at $H$ and $G$, respectively. Prove that $E$, $F$, $G$, $H$ lie on the circumference of a circle whose centre is $P$.
The circumcircle of the triangle $PDC$ intersects $BC$ and $AD$ at $E$ and $F$, respectively. The circumcircle of the triangle $PAB$ cuts $BC$ and $AD$ at $H$ and $G$, respectively. Prove that $E$, $F$, $G$, $H$ lie on the circumference of a circle whose centre is $P$.