Points A and B are marked on the circle with center O, so that the angle AOB is 60 degrees.

Points A and B are marked on the circle with center O, so that the angle AOB is 60 degrees. The height ОC is drawn to the side AB of the triangle AOB. Find AC if the radius of the circle is 22 cm.

The AOB triangle is isosceles, because AO = OB = R = 22 cm.

The OS height of an isosceles triangle is also the bisector of the AOB angle.

Angle AOC = angle COB = 60: 2 = 30 °.

Consider the AOC triangle and define the AOC.

sin of angle AOC = AC / AO;

AC = AO * sin 30 °;

AC = 22 * 1/2;

AC = 11 cm.

Answer: The AC side is 11 cm.