MathDB

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.

Problem Statement