Online Geometry
Problem 758: Equilateral Triangle, Cevians, Trisection
of sides,
Congruence, Perpendicular, 90 Degrees. Level: High School, College,
Mathematics Education

The figure shows an equilateral triangle ABC with
AE = BD = AB/3. If the cevians AD and CE meet at F, prove that BF is perpendicular
to CE. This entry contributed by Ajit Athle.