Geometry

Question Analysis

The main focus is to apply the Secant - Secant Rule. We are given expressions for the lengths of segments of the secant lines and , and we need to set up an equation using the rule to solve for , and then find the length of .

 

Key Concept Explanation

Secant - Secant Rule: If two secant lines are drawn from an external point to a circle, intersecting the circle at points and respectively, then . In this case, if two secant lines are drawn from an external point to a circle, then .

 

Step - by - Step Solution

1. Set up the equation using the rule:

We know that , , , and .

According to the Secant - Secant Rule,