Geometry

Question Analysis

The main focus is applying the Tangent - chord theorem. Given that is tangent to the circle at and the angle between the tangent and the chord is , we need to find the measure of the minor arc .

 

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. We know that the angle between the tangent and the chord is , and this angle intercepts the minor arc .

2. According to the tangent - chord theorem , where .

3. To find , we solve the equation for

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