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(B) To find the area of the largest triangle inscribed in a semi-circle,we consider the base of the triangle as the diameter of the semi-circle.Let th

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$r^{2}$ sq. units

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(B) To find the area of the largest triangle inscribed in a semi-circle,we consider the base of the triangle as the diameter of the semi-circle.Let the diameter be $AB = 2r$.For the triangle to have the maximum area,its height must be the maximum possible,which is the radius of the semi-circle,$r$.Let $C$ be the vertex on the circumference such that the altitude $CD$ is perpendicular to $AB$. Here,$CD = r$.Thus,the area of the triangle $ABC = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Area $= \frac{1}{2} 	imes (2r) 	imes r = r^{2}$ sq. units.

Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is

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