In given figure XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠ AOB = 90°.

**In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ.**

**The points A(4, –2), B(7, 2), C(0, 9) and D(–3, 5) form a parallelogram. Find the length of the altitude of the parallelogram on the base AB.**

**In what ratio does the x-axis divide the line segment joining the points (–4, –6) and (–1, 7)? Find the co-ordinates of the point of division.**

**If (1, p/3) is the mid-point of the line segment joining the points (2, 0) and (0, 2/9), then show that the line 5x + 3y + 2 = 0 passes through the point (–1, 3p).**