Question

# Construct a cyclic quadrilateral ABCD such that AB=3.4 cm,BC=4.2 cm,AD=2.7 cm and ∠ABC=60∘. Then, diameter of the circle circumscribing the cyclic quadrilateral is:

A
2.2 cm
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B
4.4 cm
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C
3.3 cm
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D
5.5 cm
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Solution

## The correct option is B 4.4 cmDraw a line segment BC of length 4.2cm. Draw a line at an angle of 60o by taking BC as base and B as vertex. Cut an arc of 3.4cm from B. This arc cuts the line at point A. Join AB. Draw perpendicular bisectors of AB and BC. These perpendicular bisectors cuts each other at point O. Draw a circle of radius OB and center O, this circle touches A,B,C. Mark an arc of length 2.7cm on circle from point A. This arc cuts the circle at point D. Join ABCD. ABCD is the required cyclic quadrilateral.We know, R=a2sinAIn △ADC∠ADC=120oAC=3.8cm⇒R=AC2sinD=3.8×22×√3=2.194Diameter =2R=2×2.194=4.4cm

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