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 = 13 cm, AP = 9 cm and AQ = 11 cm, then find the length of PQ. (in cm)

6

AB = AC

PB = PR

RQ = QC

(Tangent form same point)

Now,

BP = PR = 13 - 9 = 4 cm

AB = AC = 13

CQ = RQ = 13 - 11 = 2 cm

PQ = PR + RQ = 4 + 2 = 6 cm