First slide

Maxima and minima

Question

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

Moderate

A

$An equilateral triangle of height \frac{2 r}{3}$
B

$An isosceles triangle with base equal to 2 r$
C

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

$An equilateral triangle having each of its side of length \sqrt{3} r$

Solution

$\begin{array}{l} Circum radius of Δ l e = r \\ Area of Δ^{l e} = 2 r^{2} \sin A \sin B \sin C \end{array}$
$\begin{array}{l} Maximum when A = B = C = π / 3 \Rightarrow equilateral \\ side = 2 r \sin π / 3 = \sqrt{3} r \end{array}$

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