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

May 29, 2021 | education

| **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.

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