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Question

The two adjacent sides of a cyclic quadrilateral are 2 and 5 units and the angle between them is 600.

lf the third side is 3 units, the remaining fourth side is?

A
2
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B
3
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C
4
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D
5
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Solution

The correct option is A 2
First draw ABC with AB=2,BC=5 and ABC=60o. Then find its circum center O and then draw the circle. Then from C draw an arc of radius 3 units to cut the circle at D. Join AD. We have to find AD.

ABC: Draw AEBC.
AE=2sin60o=3
and BE=2cos60o=1
So EC=4

AEC: AC2=AE2+EC2=19,
AC=19

ADC: Draw AFCD.
Let AD=x. ADC=120°(since, 180oABC)

ADF: ADF=60° ,
So,AF=xsin60o=3x/2
FD=xcos60o=x/2

AFC: AF²=AC²FC²
(3x/2)2=19(3+x/2)2
3x2/4=199x2/43x
x2+3x10=0
(x+5)(x2)=0

Side cannot have negative length , so answer is 2

Therefore, Correct Option is A

848192_38683_ans_c9373e809258479daf53d1567c815ec4.png

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