Diameter AB and chord BC are drawn in a circle with center O. Find the angle ACO if the angle ABC = 46 degrees.

Since AB is the diameter of the circle, the degree measure of the arc ABC and the arc AB are equal to 180. Then the inscribed angle ACB is 180/2 = 90, and therefore the triangle ABC is rectangular.

Then, in a right-angled triangle ABC, the angle BAC = OAC = (180 – ACB – ABC) = (180 – 90 – 46) = 44.

The AOC triangle is isosceles, since ОА = ОАС = R, then the angle АСО = ОАС = 44.

Answer: The AOC angle is 44.