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Question

A square and the an equilateral triangle are inscribed in a circle If a and b denote the length of their sides then

A
a2=b22
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B
a22=b2
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C
3b2=2a2
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D
3a2=2b2
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Solution

The correct option is D 3a2=2b2
We have to express the radius of the circle in terms of a and b.
a2=r2+r2
=2r2
r2=a22 ....(i)
ACr=cos300b2.1r=32
r=b3 or r2=b23 ...(ii)
From (i) and (ii), we have
a22=b233a2=2b2
1034476_376439_ans_cd104f4da646470bae99d6b6a0e0c87a.png

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