11.2.3 Segment Relationships in Circles (continued) Example 4 Applying the Secant-Tangent Product Theorem
If a secant and a tangent intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared. (whole · outside = tangent 2 ) The Secant-Tangent Product Theorem is used in this example to determine the length of a tangent segment. The lengths of the segments of the secant are given. Substitute the given values into the equation from the Secant-Tangent Product Theorem and solve for x , the length of the tangent. The solution yields x = 12.
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