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Question

# Construct a cyclic quadrilateral PQRS such that PQ=QR=4.3 cm and diagonals PR=6.2 cm,QS=5.8 cm. Then, radius of the circle circumscribing the quadrilateral PQRS is:

A
4.2 cm
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B
3.1 cm
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C
2.4 cm
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D
3.7 cm
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Solution

## The correct option is B 3.1 cmDraw a line segment QR of length 4.3cm. From Q make an arc of length 4.3cm. From R make an arc of length 6.2cm. Both these arcs cuts each other at point P. Join PQ and PR. Draw perpendicular bisector of line PQ and QR. The perpendiculars intersect each other at O. Draw a circle of radius OQ from O as center. This circle also touches P,Q and R.From Q mark an arc of 5.8cm, this arc cuts the circle at point SJoin PQRS, is the required quadrilateral.PQ=4.3QS=5.8cm∠SPQ=111o (measurement)Radius =a2sinAIn △PSQR=5.82sin(111o)=3.1cm

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