Let PAB be a secant to a circle intersecting the circle at A and B. Let PT be the tangent segment. If PA=9~\text{cm} and PT=12~\text{cm}, then what is AB equal to?

Explanation

By the Tangent-Secant Theorem, PT^2 = PA \times PB. We have 12^2 = 9 \times PB, so PB = 144 / 9 = 16~\text{cm}. Since PB = PA + AB, we get 16 = 9 + AB, which gives AB = 7~\text{cm}.

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