ABCD is a quadrilateral such that ∠D = 90°. A circle with centre O touches the sides AB, BC, CD and DA at P, Q, R and S, respectively. If BC = 40 cm, BP = 28 cm and CD = 25 cm, then what is the radius of the circle?

Solution (By Examveda Team)

BC = 40, BP = 28, CD 25 (given)
BQ = BP = 28
(Tangent from an external point to a circle are equal)
CQ = 40 - 28 = 12
RC = CQ = 12
(Tangent from an external point to a circle are equal)
DR = 25 - 12 = 13
Join the line OR & OS (Both are radius)
∠DSO = ∠DRO = 90°
In quadrilateral DROS
∠ROS = 360° - (90° + 90° + 90°) = 90°
Hence, DROS is a square.
Hence radius of circle = 13
∠SDR = 90° (Given)
∴ ∠ROS = 90°
Hence DROS is a square.