Problem
As shown in the diagram at left below, $\overline{XA}$ is tangent to the circle at A and a secant thought $X$ meets the circle at $B$ and $C$, with $XB<XC$. Prove that $XB<XA<XC$.
My Question
I have already solved the problem by using the power of the point, but I want to solve it another way: using angles. I know I can prove the problem by knowing that $\angle XAC$ is an obtuse angle and $\angle XBA$ is also an obtuse angle, but how do I prove that this is the case?
