In the figure, chords AE and BC intersect each other at point D.

(i) If ∠CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm; find DE.

(ii) If AD = BD, show that : AE = BC.

In the adjoining figure, O is the center of the circle and AB is a tangent to it at point B. ∠BDC = 65°. Find ∠BAO.

In the given figure, O is center of the circle and PQ is a tangent. If angle OAB = x; the measure of angle ABP; in terms of x, is :

1. x

2. 180° - 2x

3. 90° + x

4. 90° - x

In the given figure, AB is tangent to the circle with center O. If OCB is a straight line segment, the angle BAC is :

1. 40°

2. 55°

3. 35°

4. 20°