Geometry

Question Analysis

The main focus is using the fact that a tangent to a circle is perpendicular to the radius at the point of tangency. Since  is tangent to  at point , . We can then apply 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 the right - triangle  formed by the radius , the tangent segment , and the line  from the external point  to the center , we use 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 ,  m (radius) and  m (tangent segment). We need to find

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