Question : PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that $\angle \mathrm{APB}=128^{\circ}$, then $\angle \mathrm{OAB}$ is equal to:

Option 1: 72°

Option 2: 52°

Option 3: 38°

Option 4: 64°

Question : PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that $\angle \mathrm{APB}=142^{\circ}$, then $\angle \mathrm{OAB}$ is equal to:

Option 1: 31°

Option 2: 58°

Option 3: 71°

Option 4: 64°

Question : PA and PB are two tangents from a point P outside the circle with centre O at the points A and B on it. If $\angle A P B=130^{\circ}$, then $\angle O A B$ is equal to:

Option 1: 45°

Option 2: 50°

Option 3: 35°

Option 4: 65°

Question : Two equal tangents PA and PB are drawn from an external point P on a circle with centre O. What is the length of each tangent, if P is 12 cm from the centres and the angle between the tangents is 120$^\circ$?

Option 1: 24 cm

Option 2: 6 cm

Option 3: 8 cm

Option 4: cannot be determined

Question : P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the circle is:

Option 1: 10 cm

Option 2: 13 cm

Option 3: 11 cm

Option 4: 12 cm