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 in right - triangle  to find the radius .

 

Key Concept Explanation

A tangent line to a circle is perpendicular to the radius at the point of tangency. In right - triangle , with sides  (radius),  (tangent segment), and  (hypotenuse), we use the Pythagorean theorem () to solve for .

 

Step - by - Step Solution

1. In right - triangle , by the Pythagorean theorem:

Click "Show Answer" to reveal the answer and analysis