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Question

In the given figure ABCD is a quadrilateral in which D=90 A circle C(O,r) touches the sides AB , BC , CD and DA at P , Q , R and S, respectively. If BC = 38cm , CD = 25 cm  and BP =27cm then find the value of r.


Solution


Given: ABCD is a quadrilateral such that D=90
BC = 38 cm, CD = 25 cm and BP = 27 cm
From the figure,
BP = BQ = 27 cm [Tangents from an external point]
BC = 38
BQ+QC=38
27+QC=38
QC=3827
QC=11 cm
QC=11 cm=CR [Tangents from an external point]
CD = 25 cm
CR + RD = 25
11+RD=25
RD=2511
RD=14 cm
Also,
RD = DS = 14 cm
OR and OS are radii of the circle
From tangents R and S, ORD=OSD=90
Now, ORDS is a square
OR = DS = 14 cm
Thus, radius, r = 14 cm

All India Test Series

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