A triangle ABC is inscribed in a circle of radius 7√2 centered at point O

A triangle ABC is inscribed in a circle of radius 7√2 centered at point O, in which the angle B = 45 °. Find the radius of the circle circumscribed about the triangle AOC?

According to the condition, the angle ABC = 45, which rests on the arc AC, then the central angle AOC, which also rests on the arc AC, is equal to: angle AOC = 2 * ABC = 2 * 45 = 90.

Since the angle of the AOC is straight, the segment AC is the diameter of the circle circumscribed about the triangle AOC.

Then in a right-angled triangle AOH, AH ^ 2 + OH ^ 2 = OA ^ 2.

AH ^ 2 = AO ^ 2/2 = (7 * √3) ^ 2/2.

AH = 7√3 / √2 cm.

Answer: The radius of the circle is equal to AH = 7√3 / √2 cm.