Question 47
Let $ABCD$ be a cyclic quadrilateral with longest side $AB$. Let the bisectors of the angles $\angle DCB$ and $\angle ADC$ additionally intersect the circumscribed circle of the quadrilateral $ABCD$ in points $E$ and $F$. Call $G$ the intersection point of the lines $CE$ and $DF$, and $H$ the intersection point of the lines $AE$ and $BF$.
Prove that the lines $EF$ and $GH$ intersect at right angles.
Prove that the lines $EF$ and $GH$ intersect at right angles.