A tangent AB and a secant AO are drawn to a circle centered at point O. Find the radis of the circle if AB = 65, AO = 97.

Find the radius of the circle if it is known that the tangent AB = 65 and the secant AO = 97
Solution: BO – radius of a circle perpendicular to tangent AB (tangent property)
A right-angled triangle ABO is formed
BO – leg, which can be found by the Pythagorean theorem:
BO = √AO ^ 2-AB ^ 2 = √97 ^ 2-65 ^ 2 = √5184 = 72
Answer: 72