FHSS 2025 P2 Q5

The diagram shows a point \(P\) on a circle. \(PQ\) is a tangent to the circle at \(P\).
Points \(A\), \(B\) and \(C\) lie on the circle such that \(PA\) bisects angle \(QPB\).
\(QAC\) is a straight line. The lines \(QC\) and \(PB\) intersect at \(D\).

1. Prove that \(AB = AP\).[2]
2. By first showing that triangle \(CDP\) is similar to triangle \(CBA\), show that \(PA \times CD = CB \times DP\).[5]