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Question

Construct a cyclic quadrilateral ABCD such that AB=6 cm,A=60,ABD=30 and CBD=20. Then, l(BC)=?
(Round-off your answer to the nearest integer)

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Solution

  • Draw a line segment AB of length 6cm
  • From vertex A and base AB draw a line at an angle of 60o.
  • From vertex B and base AB draw a line at an angle of 30o These two lines intersect each other at point D.
  • Join AD.
  • Draw perpendicular bisector of line AD and AB. These perpendiculars bisector intersect each other at point O.
  • From center as O, draw a circle of radius OA. This circle touches D,A,B.
  • Taking DB as base and B as vertex draw a line at an angle 20o from DB. This line cuts the circle at point C.
  • Join ABCD.
ABCD is a required quadrilateral.

Length of side BC=3.9cm4cm

892164_584245_ans_3c7affaef6a34bbdbe1384650a9ed4bf.png

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