A tangent AM is drawn to a circle with center O from point A, find the radius of the circle if the angle AOM

A tangent AM is drawn to a circle with center O from point A, find the radius of the circle if the angle AOM = 60 degrees and AO = 18

From the center of the circle, point O, draw the radius OM.

Since the radius is drawn to the tangent point, the radius OM is perpendicular to the tangent AM.

Then the triangle AOM is rectangular.

In a right-angled triangle AOM, the angle AOM, by condition, is 60, then the angle OAM = (90 – 60) = 30. The leg OM of the AOM triangle lies opposite the angle 30, then OM = R = AO / 2 = 18/2 = 9 cm.

Answer: The radius of the circle is 9 cm.