In a circle of radius 6 ^ 3 centered at point O is inscribed in triangle ABC, in which angle B = 30 degrees.

In a circle of radius 6 ^ 3 centered at point O is inscribed in triangle ABC, in which angle B = 30 degrees. Find the radius of the circle circumscribed about triangle AOC

circle R = 6√3

Inscribed ∟ <B = 30 ° opposite the AC arc

The main ∟ AOC also rests on the arc AC, which means <AOC = 60 °

triangle AOC – isosceles AO = CO = R = 6√3

∟∟ at the base of the speakers are the same,

therefore the AOS triangle is equilateral,

from this comes AC = AO = CO = R = 6√3

radius of a circle circumscribed around an equilateral triangle

R = AC * √ 3/3 = 6 * √3 * √3 / 3 = 6