Point A lies on the plane tangent to the ball at a distance of 30 from the point of tangency, the radius of the ball is 16.

Point A lies on the plane tangent to the ball at a distance of 30 from the point of tangency, the radius of the ball is 16. Find the distance from point A to the center of the ball.

We know that a tangent with a radius forms a right angle, so the distance from point A to the center of the ball can be found by the Pythagorean theorem:
30 ^ 2 + 16 ^ 2 = 900 + 256 = 1156, √1156 = 34.
Answer 34



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