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 , , allowing us to use the Pythagorean theorem to determine the length of .

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Identify the sides of the right - triangle: In right - triangle ,  mi (radius) and  mi (hypotenuse). We need to find  (one of the legs).

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

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