Concurrency and Euler line locus result

If O is the circumcentre of triangle ABC with K, L and M the respective midpoints of BC, CA and AB, and points D, E and F are respectively constructed on the lines OA, OB and OC so that OD = OE = OF, then the lines DK, EL and FM are concurrent in X and the locus of X lies on the Euler line.

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Concurrency and Euler line locus result

Challenge: can you explain (prove) why the result is true? If not, click on Solution

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Michael de Villiers, 17 May 2010.