Area of the largest triangle that can be inscribed in a semi-circle of radius r unit is
A largest triangle that can be inscribed in a semi-circle of radius r units is the triangle having its base as the diameter of the semi-circle and the two other sides are taken by considering a point C on the circumference of the semi-circle and joining it by the end points of diameter A and B.
∴ ∠ C = 90° (by the properties of circle)
So, ΔABC is right angled triangle with base as diameter AB of the circle and height be CD.
Height of the triangle = r
∴ Area of largest ΔABC = (1/2)× Base × Height = (1/2)× AB × CD
= (1/2)× 2r × r = r2 sq. units
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