# A tangent of length 4√2 is drawn to a circle of radius 7 from point A; the distance from point A

A tangent of length 4√2 is drawn to a circle of radius 7 from point A; the distance from point A to the nearest point of the circle is?

Construct the radius OB to the point of tangency B. Triangle AOB is rectangular, since the radius of the circle drawn to the point of tangency is perpendicular to the tangent itself.

In a right-angled triangle AOB, according to the Pythagorean theorem, OA ^ 2 = OB ^ 2 + AB ^ 2 = 49 + 32 = 81.

ОА = 9 cm.

The shortest distance from point A to the circle is the segment AC.

AC = AO – OC = AO – R = 9 – 7 = 2 cm.

Answer: From point A to a circle of 2 cm.

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