2026 CVSS P2 Q10

The diagram shows a triangle \(ABC\) whose vertices lie on the circumference of a circle. The tangent to the circle at point \(A\) meets the line \(BC\) extended at point \(D\). Points \(E\) and \(F\) are midpoints of \(AB\) and \(AD\) respectively. Angle \(ABC=x\) and angle \(ADC=y\).

1. Prove that triangle \(EAF\) is similar to triangle \(ACD\).[4]
2. Prove that \(CD\times EF=2(AF)^2\).[3]
3. If \(E\) is the centre of the circle, prove that angle \(BAC=y\).[2]