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.

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.

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

Prove that the parallelogram circumscribing a circle is a rhombus.

A triangle ABC is drawn to circumscribe a circle of radius 3 cm. such that the segments BD and DC into which BC is divided by the point of contact D are of length 9 cm. and 3 cm. respectively (See adjacent figure). Find the sides AB and AC.