geometry

If AX = 16 and XY = 9, then what is AB?

Hello Guest!

secant-tangent theorem

For every point X outside a circle: The square of the length of the tangent from point X to the point of tangency is equal to the product of the segments of a straight line through the circle from point X to the points of intersection with the circle.

$9=\sqrt{(16-AB)\cdot 16}\\ 81=16^2-16\cdot AB\\ AB=\dfrac{16^2-81}{16}\\ \color{blue}AB=10.9375$

  !