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Question

Construct a cyclic quadrilateral ABCD in which AB=4 cm,BC=5.6 cm,AC=7.2 cm and AD=4.5 cm. If radius of the circle circumscribing the quadrilateral ABCD is r. Then 5r=?
(Round-off to the nearest integer)

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Solution

  • Draw a line segment BC of length 5.6cm.
  • From B make an arc of length 4cm.
  • From C make an arc of length 7.2cm.
  • Both these arcs cuts each other at point A.
  • Join AB and AC.
  • Draw perpendicular bisector of line BC and AB. The perpendiculars intersect each other at O.
  • Draw a circle of radius OB from O as center. This circle also touches A,B and C.
  • From A mark an arc of 4.5cm on circle.
  • Join ABCD

r=a2sinA=BD2sin(108o)=6.92×(0.95)=3.625r=18

891950_583623_ans_a039c663a1e94fb5b4f536bf0a05bb86.png

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