Question

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 (_______pi-______ root 3)units^2

Answer 1

6,12,48,36

Explanation:

Answer 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:

`a=(√(3))/(6) l`

`a=(√(3))/(6) 12\sqrt{3`

`a=(12*3)/(6)` Since√3*√3= 3

`a=(36)/(6)`

a=6

So, apothem is 6 units long.