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# ABCD is a cyclic trapezium where AB||CD. if AB=4, AD=5, BD=7, find CD

## 2 Answers

10 years ago

The answer is CD=6.

Solution: draw BE parallel to AD such that BE=5 and DE=4. Let CE=x.

then, let angle BEC=Z

so, angle ADE and angle BCD are also Z(corresponding angles and cyclic trapezium).

From triangles BED and BEC,

cos 180-z=-cos z=(4^2+5^2-7^2)/2.4.5=-(5^2+x^2-5^2)/2.5.x

triangle BED                   Triangle BEC

on solving we get x=2 . so, CD=4+X=6.

10 years ago

thankyou so much!!!

but i didnt get why you took

cos z=(4^2+5^2-7^2)/2.4.5=-(5^2+x^2-5^2)/2.5.x

triangle BED                   Triangle BEC

i think basically i donno cos funcn in obtuse triangle

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