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5

Part of 2012 India National Olympiad

Problems(1)

Indian National Mathematical Olympiad Problem 5

Source: Acute angled triangle, AD median, BE bisector, & CF altitude

2/5/2012
Let ABCABC be an acute angled triangle. Let D,E,FD,E,F be points on BC,CA,ABBC, CA, AB such that ADAD is the median, BEBE is the internal bisector and CFCF is the altitude. Suppose that ∠FDE=∠C,∠DEF=∠A\angle FDE=\angle C, \angle DEF=\angle A and ∠EFD=∠B.\angle EFD=\angle B. Show that ABCABC is equilateral.
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