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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2016 Switzerland Team Selection Test
Problem 10
Problem 10
Part of
2016 Switzerland Team Selection Test
Problems
(1)
colinear points
Source: Swiss IMO TST 2016. Problem 10
7/27/2017
Let
A
B
C
ABC
A
BC
be a non-rectangle triangle with
M
M
M
the middle of
B
C
BC
BC
. Let
D
D
D
be a point on the line
A
B
AB
A
B
such that
C
A
=
C
D
CA=CD
C
A
=
C
D
and let
E
E
E
be a point on the line
B
C
BC
BC
such that
E
B
=
E
D
EB=ED
EB
=
E
D
. The parallel to
E
D
ED
E
D
passing through
A
A
A
intersects the line
M
D
MD
M
D
at the point
I
I
I
and the line
A
M
AM
A
M
intersects the line
E
D
ED
E
D
at the point
J
J
J
. Show that the points
C
,
I
C, I
C
,
I
and
J
J
J
are aligned.
aligned points
geometry