Question 8

8.1 O is the centre of the circle.. KOM bisects chord LN and   MNO = 26°    K and P are points on the circle with NKP = 32° . OP is drawn.

8.1.1 Determine, giving reasons, the size of:

(a)  Ô2 (2)

(b) Ô1 (4)

8.1.2 Prove, giving reasons, that KN bisects OKP. (3)

8.2 In ABC, F and G are points on sides AB and AC respectively. D is a point on GC such that D1 = B .

8.2.1 If AF is a tangent to the circle passing through points F, G and D, then prove, giving reasons, that FG || BC. (4)

8.2.2 If it is further given that and GC = x + 9, then GC = x + 9, then calculate then value of x.

[17]

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