From an external point A, two tangents AB and AC have been drawn to a circle touching the circle at B and C respectively. P and Q are points on AB and AC respectively such that PQ touches the circle at R. If AB = 11 cm, AP = 7 cm and AQ = 9 cm, then find the length of PQ (in cm).

6

Tangents drawn from same external point are equal in lengths.

AB = AC, BP = PR and CQ = RQ

= AB = AC = 11 cm

= BP + AB - AP = 11 - 7 = 4 cm

= CQ = AC - AQ = 11 - 9 = 2 cm

= BP + CQ = 4 + 2 = 6 cm

= BP + CQ = PR + RQ = 6 cm

= PR + RQ = PQ = 6 cm

Therefore, the length of PQ is 6 cm.