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MathNet 2010 — Part 06 Question 29

Math Olympiad Vault · MathNet 2010 — Part 06

Question 29

Let it be $H$ the height point of a sharp triangle $ABC$ and $D$ a point inside a triangle $ABH$. a parallel to a line $AH$ through a point $D$ Seka Side $BC$ and $AB$ in points $K$ and $L$. a parallel to a line $BH$ through a point $D$ it cuts a distance $AC$ and $AB$ in points $M$ and $N$. Prove that points $C$, $D$ and $H$ lie on the same line if the points $K$, $L$, $M$ and $N$ They lie on the same circle.