Choose the correct answer and give justification for each.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80^o, then ∠POA is equal to

A. 50^o

B. 60^o

C. 70^o

D. 80^o

Choose the correct answer and give justification for each.

From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is

A. 7 cm

B. 12 cm

C. 15 cm

D. 24.5 cm

Choose the correct answer and give justification for each.

If AP and AQ are the two tangents a circle with centre O so that ∠POQ = 110°, then ∠PAQ is equal to

A. 60^o

B. 70^o

C. 80^o

D. 90^o

Choose the correct answer and give justification for each.

In the figure XY and X¹Y¹ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X¹Y¹ at B then ∠AOB =

A. 80^o

B. 100^o

C. 90^o

D. 60^o

Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.