MathNet 2023-part-01 — 191 problems (EN–VI) Question 137

Given is an acute triangle $ABC$ with incenter $I$ and the incircle touches $BC$, $CA$, $AB$ at $D$, $E$, $F$. The circle with center $C$ and radius $CE$ meets $EF$ for the second time at $K$. If $X$ is the $C$-excircle touchpoint with $AB$, show that $CX$, $KD$, $IF$ concur.

(Kristyan Vasilev)