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National and Regional Contests
Czech Republic Contests
Czech and Slovak Olympiad III A
2006 Czech and Slovak Olympiad III A
4
4
Part of
2006 Czech and Slovak Olympiad III A
Problems
(1)
find the locus of centroid of a triangle
Source: Czech and Slovak third round,2006,p4
3/3/2012
Given a segment
A
B
AB
A
B
in the plane. Let
C
C
C
be another point in the same plane,
H
,
I
,
G
H,I,G
H
,
I
,
G
denote the orthocenter,incenter and centroid of triangle
A
B
C
ABC
A
BC
. Find the locus of
M
M
M
for which
A
,
B
,
H
,
I
A,B,H,I
A
,
B
,
H
,
I
are concyclic.
geometry
incenter
geometry proposed