Given a triangle ABC and a circle circumscribed about it. Angle A = 40 degrees

Given a triangle ABC and a circle circumscribed about it. Angle A = 40 degrees. The center of the circle lies on the AC side. We need to find other angles of the triangle.

Since point O, the center of the circle, lies on the AC side of the triangle, the OC side is the diameter of the circumscribed circle.

The inscribed angle ABC rests on the arc AC, the degree measure of which is 180, then the inscribed angle ABC = 180/2 = 90, and then the triangle ABC is rectangular.

Angle ACB = (90 – BAC) = (90 – 40) = 50.

Answer: The angles of the triangle ABC are 40, 50, 90.