In the adjoining figure the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions.

(1) What is the measure of ∠CAB ? Why?

(2) What is the distance of point C from line AB? Why?

(3) d(A,B) = 6 cm, find d(B,C).

(4) What is the measure of ∠ABC ? Why?

In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then

(1) What is the length of each tangent segment?

(2) What is the measure of ∠MRO?

(3) What is the measure of ∠MRN?

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON.

What is the distance between two parallel tangents of a circle having radius4.5 cm ? Justify your answer.