JEE Main202126 Feb 2021Evening ShiftMathematicsApplication of DerivativesActual
The triangle of maximum area that can be inscribed in a given circle of radius ' r ' is :
Options
- AAn equilateral triangle having each of its side of length 3 r .
- BAn isosceles triangle with base equal to 2 r .
- CAn equilateral triangle of height 2 r 3 .
- DA right angle triangle having two of its sides of length 2 r and r .
Correct answer
A. An equilateral triangle having each of its side of length 3 r .
Step-by-step solution
h = r sin θ + r base = B C = 2 r cos θ θ ∈ 0 , π 2 Area of Δ A B C = 1 2 B C . h Δ = 1 2 2 r cos θ . r sin θ + r = r 2 cos θ . 1 + sin θ d Δ d θ = r 2 cos θ d d θ 1 + sin θ + 1 + sin θ d d θ cos θ d Δ d θ = r 2 cos θ 0 + cos θ + 1 + sin θ - sin θ d Δ d θ = r 2 cos 2 θ - sin θ - sin 2 θ d Δ d θ = r 2 1 - sin 2 θ - sin θ - sin 2 θ = r 2 1 - sin