Draw circles with centres A, B and C each of radius 3 cm, such that each circle touches the other two circles.

In figure 3.89, line l touches the circle with centre O at point P. Q is the mid point of radius OP. RS is a chord through Q such that chords RS || line l. If RS = 12 find the radius of the circle.

In figure 3.90, seg AB is a diameter of a circle with centre C. Line PQ is a tangent, which touches the circle at point T. seg AP line PQ and seg BQ line PQ. Prove that, seg CP ≅seg CQ.

Prove that any three points on a circle cannot be collinear.

In figure 3.91, line PR touches the circle at point Q. Answer the following questions with the help of the figure.

(1) What is the sum of ∠ TAQ and∠ TSQ?

(2) Find the angles which are congruent to ∠ AQP.

(3) Which angles are congruent to ∠QTS ?

(4) ∠ TAS = 65°, find the measure of ∠TQS and arc TS.

(5) If ∠AQP = 42°and ∠SQR = 58° find measure of ∠ATS.