Question

`A B` is a diameter of a circle and `C` is any point on the circle. Show that the area of ` A B C` is maximum, when it is isosceles.
A. the area of `DeltaABC` is maximum when it is isosceles
B. the area of `Delta ABC` is minimum whne it is isosceles
C. the perimeter of `DeltaABC` is minimum when it is isosceles
D. None of the above

Answer 1

Correct Answer - A
Clearly, `angleC = 90^(@)` as angle in semi-circle is right angled. Now, area of triangle is maximum when AC=BC.
i.e., Triangle is right angled isosceles.