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In the given figure, ABCD is a quadrilat...

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.

Text Solution

Verified by Experts

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`
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