An equilateral triangle with side lengths equal to units is inscribed in a circle. half a side length of the equilateral triangle is units, so the apothem is units long and the radius of the circle is units long. each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or root 3)units^2

The side of an equilateral triangle inscribed in a circle is √3*r. So,

l=√3*r Where l= side of equilateral triangle and r= radius of circle.

Given the side length: l= 12√3. So, plug in l=12√3 in the above formula.

12√3= √3*r

So, r= 3 (Dividing each sides by √3).

So, the radius of the circle is 3 units long.

Formula to find the apothem is:

Since√3*√3= 3

a=6

So, apothem is 6 units long.

you can use a^2+ b^2=c^2

the answer is c hope this