Question

$AB$ is a diameter of a circle and $C$ is any point on the circumference of the circle. Then

• A. The area of $△ABC$ is maximum when it is isosceles
• B. The area of $△ABC$ is minimum when it is isosceles
• C. The perimeter of $△ABC$ is maximum when it is isosceles
• D. None of these

Answer 1

The correct option is A The area of $△ABC$ is maximum when it is isosceles

$\because$ Area of triangle $=\frac{1}{2}($Base$\left)\right($Height$)$

Area of triangle is maximum if height of the triangle is maximum.

We know that height is maximum when the triangle is isosceles.

Hence area of $△ABC$ is maximum when it is isosceles