MathDB
Indian RMO 2011: Question 1

Source:

December 4, 2011

Problem Statement

Let ABCABC be a triangle. Let D,E,FD, E, F be points respectively on the segments BC,CA,ABBC, CA, AB such that AD,BE,CFAD, BE, CF concur at the point KK. Suppose BDDC=BFFA\frac{BD}{DC} = \frac {BF}{FA} and ∠ADB=∠AFC\angle ADB = \angle AFC. Prove that ∠ABE=∠CAD\angle ABE = \angle CAD.
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