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MathNet 2024-part-01 — 168 problems (EN–VI) Question 110

Math Olympiad Vault · MathNet 2024-part-01 — 168 problems (EN–VI)

Question 110

Points $D$ and $E$ are on sides $BC$ and $AC$ of $\triangle ABC$. Lines $AD$ and $BE$ intersect at point $S$. Point $F$ is on side $AB$ and lines $FE$ and $FD$ intersect line $l$ passing through $C$ and parallel to $AB$ at points $P$ and $Q$. Prove that if $CP = CQ$, then the points $C$, $S$ and $F$ lie on the same line.