Question 4
Area of the largest triangle that can be inscribed in a semi – circle of radius r units is:
(A) r2squnits (B) 12r2squnits (C) 2r2squnits (D) √2r2squnits
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Solution
Takea 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 ΔABC =12×(base)(height)
So, ΔABCis right angled triangle.
∴AreaoflargestΔABC=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.