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).
Answer & explanation
Correct answer: option 4
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.