Lengths of arcs
Source: 2019 Second Round - Poland
July 8, 2019
geometryarcscyclic quadrilateral
Problem Statement
A cyclic quadrilateral is given. Point lie on the segment , points on the segment , points on the segment and points on the segment . Moreover, points lie on a circle in that order. Denote by the lengths of the arcs of the circle not containing points , respectively. Prove that
\begin{align*}
a+c=b+d.
\end{align*}