Let us denote $\prod = \{(x, y) | y > 0\}$. We call a semicircle in $\prod$ with center on the $x-\text{axis}$ a semi-line. Two intersecting semi-lines determine four semi-angles. A bisector of a semi-angle is a semi-line that bisects the semi-angle. Prove that in every semi-triangle (determined by three semi-lines) the bisectors are concurrent.