2026 ZHSS P2 Q9

The diagram shows a circle passing through the vertices of triangles \(XYZ\) and \(WXY\). \(MN\) is a tangent to the circle at \(Y\) and the chord \(XZ\) is parallel to the tangent \(MN\). The chords \(WY\) and \(XZ\) intersect at \(V\).

1. Prove that triangle \(XYZ\) is an isosceles triangle.[2]
2. Show that triangle \(YXW\) is similar to triangle \(YVX\).[3]
3. Given that \(WY\) is the diameter of the circle and the ratio of \(WX:XY=3:4\), find the ratio of \(ZY:ZX\).[3]