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
.
