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In the given figure, a circle with centre `O`, is inscribed in a quadrilateral `ABCD` such that it touches the side `BC`, `AB`, `AD` and `CD` at points `P`, `Q`, `R` and `S` respectively. If `AB=29cm`, `AD=23cm`, `/_B=90^(@)` and `DS=5cm` then find the radius of the circle.

Text Solution

Verified by Experts

`POQB` is a square , since `/_PBQ=/_BQO=/_BPO=90^(@)`, `OP=OQ=r`.
`:.r=OQ=QB`.
We know that tangents to a circle from an exterior point are equal.
`:.DS=DR`, `AR=AQ`.
Now, `AR=AD-DR=AD-DS=(23-5)cm=18cm`
and `r=QB=AB-AQ=AB-AR=(29-18)cm=11cm`.
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