An equilateral triangle that can fit in a circle has the largest area of all triangles that can be placed in a circle.

Now for an equilateral triangle with sides a, the area is given by (sqrt 3 / 4)*a^2

The radius of the circumscribed circle is a / sqrt...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

An equilateral triangle that can fit in a circle has the largest area of all triangles that can be placed in a circle.

Now for an equilateral triangle with sides a, the area is given by (sqrt 3 / 4)*a^2

The radius of the circumscribed circle is a / sqrt 3.

Now we have a circle of radius 12.

Therefore a / sqrt 3 = 12

=> a = 12 * sqrt 3

Now the area of a triangle with side 12/ sqrt 3 is

=> (sqrt 3 / 4)*(12 * sqrt 3) ^2

=> (sqrt 3 / 4)* (144 * 3)

=> (144*sqrt 3* 3/ 4)

=> 108*sqrt 3

**The area of the largest triangle that can be inscribed in a circle of radius 12 is 108*sqrt 3.**