MathDB

Beautiful problem on midlines and isogonal

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

April 24, 2023

geometryisogonal conjugatesmidlineisogonal linessine chasingangle bisector

Problem Statement

Points

A_1

B_1

C_1

are midpoints of sides

BC

AC

AB

of triangle

ABC

. On midlines

C_1B_1

and

A_1B_1

points

E

and

F

are chosen such that

BE

is the angle bisector of

AEB_1

and

BF

is the angle bisector of

CFB_1

. Prove that bisectors of angles

ABC

and

FBE

coincide.
[I]Proposed by F. Baharev