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Quadrilateral ABCD with ∠D = 90° has an inscribed circle of radius r touching AB, BC, CD, DA at P, Q, R, S. BC = 38 cm, CD = 25 cm and BP = 27 cm. Find r.

Class 10Tangent Lengths and IncirclesGeometry
  • A27 cm
  • B14 cm
  • C11 cm
  • D12.5 cm

Step-by-Step Solution

BQ = BP = 27, so CQ = 38 − 27 = 11 = CR. Then DR = 25 − 11 = 14. With ∠D = 90°, ORDS is a square, so r = DR = 14 cm.
Answer: B) 14 cm

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