In the given figure, ABCD is a quadrilateral in which `/_D = 90^@`. A – InterviewSolution

InterviewSolution

1.	In the given figure, ABCD is a quadrilateral in which `/_D = 90^@`. A circle C(O,r) touches the side AB, BC, CD and DA at P,Q,R and S, respectively. If BC= 38 cm, CD = 25 cm and BP = 27 cm, then find the value of r.
Answer» We can create a diagram with the given details. Pleae refer to video for the diagram. We know, length of tangents from any common point outside a circle are always equal. `:. OS = RD = r` `RC = CD-RD = 25-r` Also, `CQ = RC = 25-r` `BQ = BC - CQ = 38-25-r = 13+r` Now, `BP = BQ = 13+r` It is given that `BP =27cm` `:. 13+r = 27 => r = 14cm`

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