Question

ABCD is a quadrilateral such that angle D is 90°. A circle C(0,r) touches the sides AB, BC, CD and DA at P,Q,R and S respectively. If BC=38cm, CD=25cm and BP=27cm, then find r

Answer 1

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Answer 2

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Properties used:

A tangent is perpendicular to the radius.

The tangent segments to a circle from same external point are equal.

Answer:

BP=27

therefore, BQ=27 (property 2)

so QC=38-27=11

therefore, CR=11

so RD=25-11=14

in quad. ORDS

ang.D=90

ang.R=90 (prop. 1)

OR=OS

therefore,ORDS is a square

therefore,

OS=RD

radius=RD

r=14

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