Point Y is on a circle and point P lies outside the circle such that PY is tangent to the circle. Point A is on the circle such that segment PA meets the circle again at point B. If PA = 15 and PY = 9, then what is AB?

We can use the secant-tangent theorem, here....specifically........

PA * PB = (PY)^2

15* PB = (9)^2

15 * PB = 81 divide both sides by 15

PB = 81 / 15

PB = 27 / 5

So...AB = PA - PB = 15 - 27/5 = 45/5 - 27/5 = 18/5

Typo in the last line Chris. 15 = 75/5 so: PB = 75/5 - 27/5 = 48/5

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