## 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.