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Area of a quadrilateral is 3/4*root3. The radius of circle circumscribing the quad. is 1. if AB=1 BD=root3 then BC.CD=?

Area of a quadrilateral is 3/4*root3.
The radius of circle circumscribing the quad. is 1.
if AB=1 BD=root3
then BC.CD=?

Grade:9

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
clearly
\\\angle BOD=2C \\cos2C={1^2+1^2-\sqrt3^2 \over 2.1.1}=-{1 \over 2} \\C=60 \\A=180-C=120 \\$in $\Delta ABD \\cos120={AD^2+1-\sqrt3^2 \over 2.AD.1} \\=>AD=1 \\\DeltaABCD=\DeltaADB+BCD \\3\sqrt3/4=1/2.1.1sin120+1/2.BC.CD.sin60 \\=>BC.CD=2
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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