IMO Shortlist 2021 G4
IMO Shortlist 2021 G4 is a plane geometry problem from the IMO Shortlist 2021, Geometry G4: A cyclic quadrilateral and the tangent at D.
Problem
Let $ABCD$ be a quadrilateral inscribed in a circle $\Omega$. Let the tangent to $\Omega$ at $D$ intersect the rays $BA$ and $BC$ at points $E$ and $F$, respectively. A point $T$ is chosen inside the triangle $ABC$ so that $TE \parallel CD$ and $TF \parallel AD$. Let $K \neq D$ be a point on the segment $DF$ such that $TD = TK$. Prove that the lines $AC$, $DT$ and $BK$ intersect at one point.
Source IMO Shortlist 2021, Geometry G4
The diagram
Drag any point and the whole construction follows. 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.