The triangle of maximum area that can be inscribed in a given circle of radius ‘r’ is

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An equilateral triangle of height 2r3

An isosceles triangle with base equal to 2r

A right angle triangle having two of its sides of length 2r and r

An equilateral triangle having each of its side of length 3r

answer is D.

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Detailed Solution

Circum radius of Δle=r Area of Δle=2r2sinAsinBsinC Maximum when A=B=C=π/3 ⇒ equilateral side =2rsinπ/3=3r

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