
10.1In the diagram, O is the centre of the circle and P is a point on the circumference of the circle. Arc AB subtends ∠AOB at the centre of the circle and ∠APB at the circumference of the circle.
Use the diagram to prove the theorem that states that ∠AOB = 2∠APB(5) 
10.2In the diagram, O is the centre of the circle and P, Q, S and R are the points on the circle. PQ = QS and ∠QRS = y. The tangent at P meets SQ produced at T. OQ intersects PS at A.

10.2.1Give a reason why ∠P_{2} = y(1)

10.2.2Prove that PQ bisects ∠TPS(4)

10.2.3Determine ∠POQ in terms of y.(2)

10.2.4Prove that PT is a tangent to the circle that passes through points P, O and A.(2)

10.2.5Prove that ∠OAP = 90°(5)

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