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CTK Exchange
alexb
Charter Member
1877 posts |
Aug-21-06, 07:15 PM (EST) |
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"Orthogonality in Isosceles Triangle"
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In triangle ABC, O is the circumcenter, D is the midpoint of AB, E is the centroid of triangle ACD. Prove that EO is perpendicular to CD iff AB = AC. The problem comes from Honsberger's From Erdos to Kiev (pp. 230-234). There are two analytic solutions and a mention of alternative solutions at Crux Mathematicorum, 1991, 105 and 228, to which I have no access. I am interested in a synthetic solution. Thank you, Alex
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