Geometry

Question Analysis

The main focus is correctly applying the Tangent - chord theorem. We need to first determine the correct arc measure based on the given angle between the tangent and the chord , and then use the relationship between the arcs to set up an equation 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. Given that the angle between the tangent and the chord is . So the measure of the major arc is .

2. The minor arc's measure is then , and the expression for the minor arc is

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