Find the distance from point A to the nearest point of a circle with center O of radius R if OA = 12cm, and radius = 8

Let the segment OA intersect the circle at the point M.

We construct the tangent MH through the point M.

The radius OM drawn to the tangent point is perpendicular to the tangent MH, and since the point M lies on the straight line OA, the segment AM is perpendicular to the tangent MH.

Then the segment AM is the closest distance from point A to the circle.

AM = OA – R = 12 – 8 = 4 cm.

Answer: From point A to a circle of 4 cm.