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A right triangle is drawn in a semi circle of radius $\frac{1}{2}$ with one of its legs along the diameter. If the maximum area of the triangle is M, then the value of 4M is ____

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answer is 1.

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Detailed Solution

$B C \times C E = A C \times C D \Rightarrow (B C) (C E) = x (1 - x)$

$∴ B C = \sqrt{x (1 - x)} \Rightarrow Area$

$Δ = \frac{x \sqrt{x - x^{2}}}{2}$

If $\frac{d Δ^{2}}{d x} = 0 \Rightarrow x = 3 / 4$ which is the point of maxima.

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