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5

Part of 2010 Iran MO (2nd Round)

Problems(1)

Iran National Math Olympiad-Day 2-Problem 5

Source:

4/30/2010
In triangle ABCABC we havev ∠A=π3\angle A=\frac{\pi}{3}. Construct EE and FF on continue of ABAB and ACAC respectively such that BE=CF=BCBE=CF=BC. Suppose that EFEF meets circumcircle of △ACE\triangle ACE in KK. (K≢EK\not \equiv E). Prove that KK is on the bisector of ∠A\angle A.
geometrycircumcircletrigonometryvectorangle bisectorIran