2026 CCHY P1 Q13

In the diagram, \(A\), \(B\), \(C\) and \(D\) lie on a circle. The line \(XDY\) is the tangent to the circle at \(D\) and the line \(XAN\) is the tangent to the circle at \(A\). The lines \(AB\) and \(DC\) are produced to meet at \(E\) and angle \(XDA=\) angle \(BCE\).

1. Prove that \(XY\) is parallel to \(AE\).[2]
2. Prove that triangle \(DAB\) is isosceles.[2]
3. Prove that \(DA^2=XD\times AB\).[3]