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 : 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 $\angle {APB}=100^{\circ}$, then $\angle {OAB}$ is equal to:

Option 1: $45^{\circ}$

Option 2: $35^{\circ}$

Option 3: $70^{\circ}$

Option 4: $50^{\circ}$

Question : A tangent is drawn from an external point 'A' to a circle of radius 12 cm. If the length of the tangent is 5 cm, then the distance from the centre of the circle to point 'A' is:

Option 1: 17 cm

Option 2: 9 cm

Option 3: 7 cm

Option 4: 13 cm

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 : 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°