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In geometry, Monge's theorem states that for any three nonoverlapping circlesof distinct radii in the two dimensional analytical plane equipped with theEuclidean metric, none of which is completely inside one of the others, theintersection points of each of the three pairs of external tangent lines arecollinear. So, it is clearly observed that Monge's theorem is an application ofDesargues' theorem. Our main motivation in this study is to show whether Mongetheorem is still valid even if the plane is equipped with the metrics alpha andLp.

Does The Monge Theorem Apply To Some Non-Euclidean Geometries ?