A tangent is drawn to a circle of radius 5 cm at point B. Point A is marked on the tangent at a distance

A tangent is drawn to a circle of radius 5 cm at point B. Point A is marked on the tangent at a distance of 12 cm from point B. Find the distance from point a to the center of the circle.

The radius of the circle drawn to the tangent point of the tangent is perpendicular to it.

This means that the OB radius is perpendicular to ВA.

The OBA triangle is rectangular. By the Pythagorean theorem:

OA² = OB² + AB²; OB = 5cm; AB = 12 cm;

OA² = 5² + 12² = 25 + 144 = 169 (cm²);

OA = √169 = 13 (cm).