15, 30, 60, 120 …… are in G.P. (Geometric Progression).

(a) Find the nth term of this G.P. in terms of n.

(b) How many terms of the above G.P. will give the sum 945 ?

In the given diagram, O is the centre of the circle. PR and PT are two tangents drawn from the external point P and touching the circle at Q and S respectively. MN is a diameter of the circle. Given ∠PQM = 42° and ∠PSM = 25°.

Find :

(a) ∠OQM

(b) ∠QNS

(c) ∠QOS

(d) ∠QMS

Use graph sheet for this question.

(a) Plot A(0, 3), B(2, 1) and C(4, -1).

(b) Reflect point B and C in y-axis and name their images as B' and C' respectively. Plot and write coordinates of the points B' and C'.

(c) Reflect point A in the line BB' and name its images as A'.

(d) Plot and write coordinates of point A'.

(e) Join the points ABA'B' and give the geometrical name of the closed figure so formed.