MathDB

9.5

Part of 2001 Saint Petersburg Mathematical Olympiad

Problems(1)

Beautiful problem on midlines and isogonal

Source: St. Petersburg MO 2001, 9th grade, P5

4/24/2023
Points A1A_1, B1B_1, C1C_1 are midpoints of sides BCBC, ACAC, ABAB of triangle ABCABC. On midlines C1B1C_1B_1 and A1B1A_1B_1 points EE and FF are chosen such that BEBE is the angle bisector of AEB1AEB_1 and BFBF is the angle bisector of CFB1CFB_1. Prove that bisectors of angles ABCABC and FBEFBE coincide.
[I]Proposed by F. Baharev
geometryisogonal conjugatesmidlineisogonal linessine chasingangle bisector