QExample 3 : PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig. 10.10). Find the length TP.

Solution : Join OT. Let it intersect PQ at the point R. Then $\u2206$ TPQ is isosceles and TO is the angle bisector of $\angle $PTQ . So, OT $\perp $PQ and therefore, OT bisects PQ which gives PR = RQ = 4 cm.