Denote by
midpoint of side
in an isosceles triangle
with
. Take a point
on a smaller arc
of circumcircle of triangle
. Denote by
point inside of angle
such that
and
.
Prove that
does not depend on choice of
.
Author: unknown author, Canada
%V0
Denote by $M$ midpoint of side $BC$ in an isosceles triangle $\triangle ABC$ with $AC = AB$. Take a point $X$ on a smaller arc $\widehat{MA}$ of circumcircle of triangle $\triangle ABM$. Denote by $T$ point inside of angle $BMA$ such that $\angle TMX = 90$ and $TX = BX$.
Prove that $\angle MTB - \angle CTM$ does not depend on choice of $X$.
Author: unknown author, Canada
Školjka