Geometry

Question Analysis

The main focus is applying the Secant - Tangent Rule. We know the lengths of segments and of a secant line from an external point to the circle, and is expressed in terms of . We need to find the value of and then the length of .

 

Key Concept Explanation

Secant - Tangent Rule: If a tangent line and a secant line are drawn from an external point to a circle, with the tangent length , the external part of the secant , and the entire secant length , then . In our case, considering in relation to the secant and its part , we have .

 

Step - by - Step Solution

1. Set up the equation using the rule:

We know and , and .

According to the Secant - Tangent Rule,

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