The angle at the base of an isosceles triangle is 15 degrees, and the base is 8.

The angle at the base of an isosceles triangle is 15 degrees, and the base is 8. The diameter of the circle circumscribed about the triangle is?

Let’s determine the value of the angle ABC.

Angle ABC = 180 – BAC – BCA = 180 – 15 – 15 = 150.

Then the degree measure of the larger arc AC = 2 * ABC = 2 * 150 = 300.

Then the degree measure of the arc ABC = 360 – 300 = 60.

The central angle AOC is equal to the degree measure of the arc ABC, the angle AOC = 60.

Then the triangle AOC is equilateral, since OA = OC = R, and the angle AOC = 60.

ОА = ОC = AB = R = 8 cm.

AD = 2 * R = 2 * 8 = 16 cm.

Answer: The diameter of the circle is 16 cm.