Question

AB is a diameter of a circle and C is a point on the circumfrence of the circle then

• A. Area of the $\Delta ABC$ is maximum when it is isosceles
• B. Area of the $\Delta ABC$ is minimum when it is isosceles
• C. The perimeter of $\Delta ABC$ is minimum when it is isosceles
• D. The perimeter of $\Delta ABC$ is maximum when it is isosceles

Answer 1

The correct option is A Area of the $\Delta ABC$ is maximum when it is isosceles

area of $\Delta =\left|\begin{array}{cc}r& 0\\ -r& 0\\ r\sin \theta & r\cos \theta \\ r& 0\end{array}\right|$
$=-r^2\cos \theta -r^2\cos \theta$
area of $\Delta =-2r^2\cos \theta$
To maximise area of $\Delta \to \theta =0^o$
$C=(0,r)$
$AC=BC$
So it is on isosceles $\Delta$