A chord AB is drawn in a circle centered at point O. Through points A and B are drawn tangents to the circle

A chord AB is drawn in a circle centered at point O. Through points A and B are drawn tangents to the circle, intersecting at point P. Find the degree measure of the angle AOB, if the angle APO is 15 degrees.

Let us draw to the points of tangency A and B the radii of the circle OA and OB, which, by the property of the tangent to the circle, form an angle with the tangent. Angle ОАР = ОВР = 90.

Consider a quadrangle OAРB, the sum of the internal angles of which is 360, then the angle AOB = (360 – AРВ – OВР – OAР) = (360 – 15 – 90 – 90) = 165.

Answer: The central angle of the AOB is 165.