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Question

Construct a cyclic quadrilateral ABCD such that AB=3.4 cm,BC=4.2 cm,AD=2.7 cm and ABC=60. Then, sum of the lengths of the diagonals is:

A
8.3 cm
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B
9.2 cm
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C
10.6 cm
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D
7.1 cm
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Solution

The correct option is A 8.3 cm
  • Draw 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.

l(AC)=3.8cm (measurement)
l(BD)=4.5cm (measurement)
AC+BD=8.3cm

891970_583748_ans_f979339896084bb0bda134e4cd427c10.png

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