1. 10.1
    In 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.

    Diagram

    Use the diagram to prove the theorem that states that ∠AOB = 2∠APB
    (5)
    1. 10.2
      In 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.

      Diagram
      1. 10.2.1
        Give a reason why ∠P2 = y
        (1)
        1. 10.2.2
          Prove that PQ bisects ∠TPS
          (4)
          1. 10.2.3
            Determine ∠POQ in terms of y.
            (2)
            1. 10.2.4
              Prove that PT is a tangent to the circle that passes through points P, O and A.
              (2)
              1. 10.2.5
                Prove that ∠OAP = 90°
                (5)
              (19)
              [{"prnt":"10","num":"10.1","answer":""},{"prnt":"10.2","num":"10.2.1","answer":""},{"prnt":"10.2","num":"10.2.2","answer":""},{"prnt":"10.2","num":"10.2.3","answer":""},{"prnt":"10.2","num":"10.2.4","answer":""},{"prnt":"10.2","num":"10.2.5","answer":""}]

              Answers

                1. 10.1
                2. 10.2.1
                3. 10.2.2
                4. 10.2.3
                5. 10.2.4
                6. 10.2.5
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