Geometry

Question Analysis

The main focus 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. We know that the angle between the tangent  and the chord  is . According to the tangent - chord theorem, this angle intercepts the minor arc , so , where .

Multiply both sides by 2 to get .

2. The major arc  and the minor arc  together make up the whole circle, which has a measure of .

So,

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