Question 19
In a convex quadrilateral $ ABCD $ the diagonal $ BD $ does not bisect the angles $ ABC $ and $ CDA $. The point $ P $ lies inside $ ABCD $ and satisfies
$$ \angle PBC=\angle DBA\quad\text{and}\quad\angle PDC=\angle BDA. $$
Prove that ABCD is a cyclic quadrilateral if and only if AP = CP.
$$ \angle PBC=\angle DBA\quad\text{and}\quad\angle PDC=\angle BDA. $$
Prove that ABCD is a cyclic quadrilateral if and only if AP = CP.