Geometry

Question Analysis

The main focus is correctly applying the Tangent - chord theorem. First, we use the theorem to find the measure of the minor arc intercepted by the angle between the tangent and the chord . Then, we set up an equation based on the relationship between the minor and major arcs to solve for .

 

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.

 

Step - by - Step Solution

1. According to the Tangent - chord theorem, since the angle between the tangent and the chord is , the measure of the minor arc is .

2. The major arc, whose measure is given by , and the minor arc together make up a full - circle, which has a measure of . So, we set up the equation

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