2026 SPS P2 Q7

In the diagram, AC is a diameter of the circle, with centre O, and the points A, B, C and D lie on the circle with radius of 9.2 cm.

AC bisects angle BCD. Angle \(DCA=32^\circ\). M is the point on DC such that DM=MC.

1. Find angle BOA. Give reasons for each step of your working.[2]
2. Show that triangle COM is similar to triangle CAB.[2]
3. Show that BC=DC.[2]
4. Find the shortest distance of BC from O.[2]