Question

A triangle is inscribed in a semi circle of radius $a$ so that one side is the bounding diameter. Then the maximum area of the triangle is

• A. $\left(\pi /4\right)a^2$
• B. $\left(1/2\right)a^2$
• C. $\left(1/4\right)a^2$
• D. $a^2$

Answer 1

The correct option is D $a^2$

area of $\Delta =\frac{1}{2}\times 2a\times DC$
To maximize area $DC=$ radius of circle
$\Delta =\frac{1}{2}\times 2a\times a$
$=a^2$