Geometry

Question Analysis

The main focus is using the property that a tangent to a circle is perpendicular to the radius at the point of tangency. Since  is tangent to  at point , , and we can use the Pythagorean theorem to find the length of .

 

Key Concept Explanation

A tangent line to a circle is perpendicular to the radius at the point of tangency. In a right - triangle formed by the radius (), the tangent segment (), and the line from the external point to the center (), we can apply the Pythagorean theorem (, where  is the hypotenuse) to find the unknown side length.

 

Step - by - Step Solution

1. Identify the sides of the right - triangle: In right - triangle ,  mm (radius) and  mm (tangent segment). We need to find  (hypotenuse).

2. Apply the Pythagorean theorem: According to the Pythagorean theorem

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