Geometry

Question Analysis

The main focus is to correctly apply the Secant - Secant Rule. We know the lengths of three segments of the secant lines starting from the external point , and we need to find the length of by setting up and solving an equation based on the rule.

 

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 . That is, for secant lines and from point , .

 

Step - by - Step Solution

1. Set up the equation using the rule:

Let the length of be ,and , so .

We know

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