What is the distance?
Posted: Fri Mar 30, 2018 10:03 pm
Let $ABC$ be a triangle with $AB=26, AC=28, BC=30$. Let $X, Y, Z$ be the midpoints of arcs $BC, CA, AB$ (not containg the opposite vertics) respectively on the circumcircle of triangle $ABC$. Let $P$ be the midpoint of arc $BC$ containing point A. Suppose, lines $BP$ and $XZ$ meet at $M$, while lines $CP$ and $XY$ meet at $N$. Find the square of the distance from $X$ to $MN$.