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About: Van Lamoen circle


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In Euclidean plane geometry, the van Lamoen circle is a special circle associated with any given triangle . It contains the circumcenters of the six triangles that are defined inside by its three medians. Specifically, let , , be the vertices of , and let be its centroid (the intersection of its three medians). Let , , and be the midpoints of the sidelines , , and , respectively. It turns out that the circumcenters of the six triangles , , , , , and lie on a common circle, which is the van Lamoen circle of .

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