Question

A triangle of maximum area is inscribed in a circle. If a side of the triangle is 20√3 then the radius of the circle is

Answer 1

The radius of the circle is 20√3.

Step-by-step explanation:

The radius of the circle can be determined by using the fact that a triangle inscribed in a circle with a given side length has its opposite angle equal to the angle subtended by the same side at the center of the circle. Since the side length of the triangle is 20√3, the opposite angle can be found using the law of sines:

sin(A)/20√3 = sin(90°)/r

Solving for r, we get:

r = 20√3/sin(A)

Substituting A = 90°, we get:

r = 20√3

Therefore, the radius of the circle is 20√3.