Geometry

Question Analysis

The key is applying the Tangent - chord theorem.

Key Concept Explanation

Tangent - chord Theorem: The measure of the angle formed by a tangent and a chord is equal to half the measure of the intercepted arc. That is, if is the angle between the tangent and the chord, and is the measure of the intercepted arc, then .

 

Step - by - Step Solution

1. Given that the angle between the tangent and the chord is . By the tangent - chord theorem, this angle intercepts the minor arc , so , with .

Multiply both sides by 2: .

2. Since the major arc and the minor arc sum to (the measure of a full circle), we have

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