Triangle ABC is inscribed in a circle centered at point O. Find the angle ACB if the angle AOB is 73 ‘.

According to the condition, the triangle ABC is inscribed in a circle centered at point O, that is, each vertex of this triangle lies on a circle, and its sides intersect it.

Inscribed corner
An inscribed angle is an angle whose vertex lies on a circle.

Thus, all angles of the triangle ABC are:

angle ABC;
angle BCA;
angle CAB

are inscribed angles in a circle centered at point O.

Central corner
The center angle is the angle whose apex coincides with the center of the circle.

So the angles are:

AOC;
BOA;
COB
represent the central corners of a circle centered at point O.

The ratio between the center and inscribed corners
The central angle is 2 times the inscribed angle if they rest on one arc, that is, their rays intersect the circle at the same points.

Thus, the angle ACB and the angle AOB equal to 73 degrees are inscribed and central, respectively, since both are based on the arc AB and therefore ACB = 1/2 AOB = 73/2 = 36.5 degrees.

Answer: the angle ACB inscribed in the circle is 36.5 degrees.