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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:
Solution
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
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