In the figure (ii) given below, O and O' are centres of two circles touching each other externally at the point P. The common tangent at P meets a direct common tangent AB at M. Prove that,

(i) M bisects AB.

(ii) ∠APB = 90°.

In adjoining figure, P and Q are the centers of two circles touching externally at R and CD is the common tangent.

If ∠CAR = 38°, then find ∠DBR.

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 140°, then ∠BAC is equal to

1. 80°

2. 50°

3. 40°

4. 30°

In the adjoining figure, O is the centre of the circle. If ∠BAO = 60°, then ∠ADC is equal to

1. 30°

2. 45°

3. 60°

4. 120°