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Question 4
Area of the largest triangle that can be inscribed in a semi – circle of radius r units is:
(A)
r2 sq units
(B) 12r2 sq units
(C) 2r2 sq units
(D) 2r2 sq units

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Solution

Take a point C on the circumference of the semi circle and join it by the end points of diameter A and B
C=90
[angle in a semi-circle is a right angle]
Area of Δ ABC
= 12×(base)(height)

So, ΔABC is right angled triangle.

Area of largest ΔABC=12×AB×CD
Inorder to have largest traingle, base of triangle will be circles diameter and maximum height can be acheived when the point c is taken just above centre. i.e. CD = radius of circle.

=12×2r×r

=r2 sq units


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