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 = 10, then what is AB?

Guest Nov 4, 2020

#1**+1 **

By Power of A Point, \(PB \cdot PA = PY^2\).

Therefore, \( PB = \frac{PY^2}{PA} = \frac{10^2}{15} = \frac{20}{3}. \)

And as a result \(AB = PA - PB\), meaning that \(AB\) is \(15 - \frac{20}{3} = \frac{25}{3}\)

xCorrosive Nov 4, 2020