The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

In Fig. 5, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.

Prove that:

(i) AB + CQ = AC + BQ

(ii) Area (Δ ABC) = 1/2 (Perimeter of ΔABC) × r

If the points A (1, -2), B (2, 3), C (-3, 2) and D (-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.

Water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minutes. Find the rate of flow of water in the pipe in km/h.