In the given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. If ∠BAQ = 30°, prove that : BD is diameter of the circle.

Chords AB and CD of a circle intersect each other at point O such that OA : OC = 4 : 7. Then OB : OD is equal to :

1. 4 : 7

2. 5 : 4

3. 7 : 4

4. 4 : 5

AC is a tangent to the given circle which touches the circle at point B. If ∠EBC = 45°; angle EDB is equal to :

1. 45°

2. 90°

3. 125°

4. 135°

In the given circle, PA is tangent and PBC is secant, PA = 8 cm and PB = 4 cm. The length of BC is :

1. 8 cm

2. 12 cm

3. 16 cm

4. 2 cm