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

IN the given figure, ABCD is a quadrilateral in which `angleADC=90^@, BC=38 cm, CD=28 cm` and `BP=25 cm`. Find the radius of the circle with centre O.

Text Solution

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Let `r` is the radius of the circle.
As `/_ADC = 90^@`
`:. OS = OR = RD = SD = r`
We know, length of tangents from any common point outside a circle are always equal.
`:. BP = BQ = 25cm`
`CQ = CR = 38-25 = 13cm`
`DR = DS = DC-CR = 28-13 = 15cm`
`:. OS = DR = 15cm`
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