A tangent line is drawn from point B to the circle with center O, A is the tangency point.

A tangent line is drawn from point B to the circle with center O, A is the tangency point. find the distance from point B to the center of the circle if the radius of the circle is 5 and the angle AOB = 60 °.

Let us draw the radius OA to the point of tangency A to the tangent BA. The radius drawn to the tangent point is perpendicular to the tangent itself. Then triangle AOB is rectangular, in which, by condition, the angle AOB is 60.

Then the angle ABO = 90 – 60 = 30.

The OA leg lies opposite an angle of 30, then the length of the AO leg is equal to half of the OB hypotenuse.

AO = ОВ / 2.

ОВ = 2 * AO = 2 * 5 = 10 cm.

Answer: From point B to the center of the circle 10 cm.