Math CentralQuandaries & Queries


Question from Nazrul, a teacher:

The circumcentre and orthocentre of a triangle are given. A point on a side of the triangle
given. A vertex of the triangle on the circumcircle is also given.
How can I draw the triangle?
Please Help me.
Thank you for answering my previous questions.


The point given on a side of the triangle is not needed. You must assume that the triangle exists and everything has been erased except the circumcenter O, orthocenter H, and vertex A (and point on a side, if you wish). You need to use two facts:
(1) the centroid G lies on the Euler Line OH 1/3 of the way from O to H.
(2) The midpoint of M of the side BC is the point on the extension of AG (with G between A and M) for which GM = 2AG.

Now BC is the line perpendicular to AH, and the rest is easy.


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