Τρίτη, 10 Οκτωβρίου 2017

2008 JBMO Shortlist G1

Two perpendicular chords of a circle, $AM, BN$ , which intersect at point $K$, define on the circle four arcs with pairwise different length, with $AB$ being the smallest of them. We draw the chords $AD, BC$ with $AD // BC$ and $C, D$ different from $N, M$ . If $L$ is the point of intersection of $DN, M C$ and $T$ the point of intersection of $DC, KL,$ prove that $\angle KTC = \angle KNL$.

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