In the diagram, LK is a diameter of the circle with centre P. RNS is a tangent to the circle at N. T is a point on NK and TP ⊥ KL. ∠PLN = x.

11.1Prove that TPLN is a cyclic quadrilateral(3)

11.2Determine. giving reasons, the size of ∠N_{1} in terms of x.(3)

11.3Prove that:

11.3.1▵KTP  ▵ KLN(3)

11.3.2KT.KN = 2KT^{2}  2TP^{2}(5)

(14)
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