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Baltic Way
1999 Baltic Way
12
12
Part of
1999 Baltic Way
Problems
(1)
Incentre, circumcentre and midpoints of AC,BC are concyclic
Source: Baltic Way 1999
12/23/2010
In a triangle
A
B
C
ABC
A
BC
it is given that
2
A
B
=
A
C
+
B
C
2AB=AC+BC
2
A
B
=
A
C
+
BC
. Prove that the incentre of
△
A
B
C
\triangle ABC
△
A
BC
, the circumcentre of
△
A
B
C
\triangle ABC
△
A
BC
, and the midpoints of
A
C
AC
A
C
and
B
C
BC
BC
are concyclic.
geometry
incenter
angle bisector
geometry proposed