Geometry

Question Analysis

The main focus is leveraging the property 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 use the Pythagorean theorem to find the radius .

 

Key Concept Explanation

A tangent line to a circle forms a right - angle with the radius at the point of contact. In right - triangle , we apply the Pythagorean theorem (, where  is the hypotenuse) to relate the radius , the tangent segment , and the line .

 

Step - by - Step Solution

1. In right - triangle , by the Pythagorean theorem, we have

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