IMO Shortlist 2021 G1
IMO Shortlist 2021 G1 is a plane geometry problem from the IMO Shortlist 2021, Geometry G1: A parallelogram with AC = BC.
Problem
Let $ABCD$ be a parallelogram such that $AC = BC$. A point $P$ is chosen on the extension of the segment $AB$ beyond $B$. The circumcircle of the triangle $ACD$ meets the segment $PD$ again at $Q$, and the circumcircle of the triangle $APQ$ meets the segment $PC$ again at $R$. Prove that the lines $CD$, $AQ$, and $BR$ are concurrent.
Source IMO Shortlist 2021, Geometry G1
The diagram
Drag any point and the whole construction follows; ▶ runs a point along its line and back. Tap a point to pin it, double-click to go back to the start. Effects redraws the figure in grayscale for print, in colour, or with the givens in focus.