The diameter AC and the chord AB, equal to the radius of the circle, are drawn in the circle.

The diameter AC and the chord AB, equal to the radius of the circle, are drawn in the circle. Find the angles of the triangle ABC.

Consider a triangle ABC inscribed in a circle.

By the condition of the problem, it is known that AC is the diameter of the circle.

Therefore, the inscribed angle ABC = 1/2 * 180 ° = 90 °.

Hence, triangle ABC is rectangular.

It is also known that AB is equal to the radius of the circle.

Therefore, AB = 1/2 * AC, since AC is the diameter.

Let O be the middle of AC. Since AC is the diameter, O is the center of the circle described around the triangle ABC.

Then we have: AB = BO = AO. This means that the ABO triangle is equilateral and its angles are 60 °.

So, we have:

ABC = 90 °, BAC = 60 °, BCA = 30 °.