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 = 11cm, AP = 7 cm and AQ = 9cm , then the length of PQ (in cm).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 6
Given :
AB and AC are two tangents from external point A
AB = 11cm, AP = 7 cm and AQ = 9cm
P and Q are points on AB and AC respectively such that PQ touches the circle at R
Calculations :
AB = AC, BP = PR and CQ = RQ
Tangents drawn from the same external points are equal in lengths
⇒ AB = AC = 11cm
⇒ BP = AB - AP = 11 - 7 = 4cm
⇒ CQ = AC - AQ = 11 - 9 = 2cm
⇒ BP + CQ = 4 + 2 = 6cm
⇒ BP + CQ = PR + RQ = 6cm
⇒ PQ = PR + RQ = 6cm