Question:
The area of the largest triangle that can be inscribed in a semi-circle of radius r, is
(a) $r^{2}$
(b) $2 r^{2}$
(c) $r^{3}$
(d) $2 r^{3}$
Solution:
The triangle with the largest area will be symmetrical as shown in the figure.
Let the radius of the circle be r.
Hence,
$a r(\Delta \mathrm{ABC})=\frac{1}{2}(r)(2 r)$
$=r^{2} s q$, unit
Therefore the answer is (a).
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