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Question

# The triangle of maximum area that can be inscribed in a given circle of radius ′r′ is:

A
A right-angle triangle having two of its sides of length 2r and r
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B
An equilateral triangle of height 2r3
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C
Isosceles triangle with base equal to 2r
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D
An equilateral triangle having each of its side of length 3r
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Solution

## The correct option is D An equilateral triangle having each of its side of length √3rTriangle of maximum area that can be inscribed in a circle is an equilateral triangle. Let △ABC be inscribed in circle, Now, in △OBD OD=rcos60∘=r2 Height =AD=3r2 Again in △ABD Now sin 60∘=3r/2AB ⇒AB=√3r

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