Question

Area of the largest circle that can be inscribed in a semicircle of radius ‘r’ units is

Answer 1

The largest circle that can be inscribed in a semicircle with radius r are we have its diameter = r.

Refer to the above attachment.

Answer 2

❁❁ Refer To Image First .. ❁❁

From image we can see that, we have a Semi-circle with Diameter CA .

→ Radius of semicircle = CB = BA = BD = Let r units .

Now, Their is a circle with Centre O inside this Semi-circle ,

→ Diameter of Circle = BD = r units .

So,

→ Radius of circle = BO = OD = (r/2) units .

Hence, Area of circle will be = π(radius)² = π(r/2)² = ( πr²/4) units².

So, Area of Largest circle inside a semi-circle of radius r is ( πr²/4) units².