Question

What is the area of an equilateral triangle inscribed in a circle with a radius of 5 inches?

Answer 1

`(50 + 50 * 1 / 2) sqrt 3 / 4`

Explanation:

`Delta ABC` is equilateral. `O` is the center.

`|OA| = 5 = |OB|`

`A hat O B = 120º = (2 pi) / 3`

Cossin Law: `|AB|^2 = 5^2 + 5^2 - 2 * 5^2 cos 120º = L^2`

`A_Delta = L^2 sqrt 3 / 4`