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 minimum when it is isosceles
• D. None of the above

Answer 1

Answer: (A)

the area of $?$ ABC is maximum when it is isosceles

Answer 2

Clearly, $\angle {C}= {90}^\circ$ as angle in semi-circle is right angled.
Now, area of triangle is maximum when A C = BC.
i.e. Triangle is right angled isosceles.