MathDB
Problems
Contests
National and Regional Contests
Chile Contests
Chile National Olympiad
2010 Chile National Olympiad
3
3
Part of
2010 Chile National Olympiad
Problems
(1)
incenter lies on a segment connecting midpoints (Chile 2010 L2 P3)
Source:
5/31/2019
The sides
B
C
,
C
A
BC, CA
BC
,
C
A
, and
A
B
AB
A
B
of a triangle
A
B
C
ABC
A
BC
are tangent to a circle at points
X
,
Y
,
Z
X, Y, Z
X
,
Y
,
Z
respectively. Show that the center of such a circle is on the line that passes through the midpoints of
B
C
BC
BC
and
A
X
AX
A
X
.
geometry
incenter
midpoints