Geometry

Question Analysis

The main focus is to use the property that a tangent to a circle is perpendicular to the radius at the point of tangency. We'll check if the triangle formed by the radius, the line segment from the external point to the point of contact, and the line from the center to the external point satisfies the Pythagorean theorem for a right - angle.

 

Key Concept Explanation

A tangent line to a circle touches the circle at exactly one point and is perpendicular to the radius at that point. We can verify if the angle between the line and the radius is  by using the Pythagorean theorem (, where  is the hypotenuse of a right - triangle).

 

Step - by - Step Solution

1. Identify the sides of the triangle: In ,  (radius), , and .

2. Apply the Pythagorean theorem: Calculate  and .

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