Question

In the given figure, the sides of the quadrilateral PQRS touches the circle at A, B, C and D. If RC = 4 cm, RQ = 7 cm and PD = 5 cm. Find the length of PQ:

Answer 1

PD = PA = 5 cm    ....(1) [Tangents from exterior point are equal in length]

QA = QB = q        ....(2) [Tangents from exterior point are equal in length]

RC = RB = r = 4 cm     ....(3) [Tangents from exterior point are equal in length]

SD = SC = s        ....(4) [Tangents from exterior point are equal in length]

RQ = RB + BQ     (given)

⇒ 7 cm =  4 + QB     ...[from (3)]

⇒ QB = 3 cm     ...(5)

∵ QA = QB = 3 cm      ...(6) [from (2) and (5)]

∴ PQ = PA + AQ

∴ PQ = 5 + 3      ....[From (1) and (6)]

∴ PQ = 8 cm