A circle inscribed in a quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q, R and S, respectively. If AS = 6 cm BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 13.
The length of two tangents drawn from an external point to a circle are equal.
In the above diagram,
CR = CQ =5 cm
BC = BQ + CQ
⇒ 12 = BQ + 5
⇒ BQ = 7 cm
⇒ BQ = BP = 7 cm
⇒ AS = AP = 6 cm
The length of AB = AP + BP = 6 + 7 = 13 cm