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National and Regional Contests
Argentina Contests
Argentina National Olympiad
1997 Argentina National Olympiad
2
2
Part of
1997 Argentina National Olympiad
Problems
(1)
ABC$ is isosceles or right when <CAM +<MCB = 90^o, M midpoint of ABC
Source: 1997 Argentina OMA L3 p2
6/11/2020
Let
A
B
C
ABC
A
BC
be a triangle and
M
M
M
be the midpoint of
A
B
AB
A
B
. If it is known that
∠
C
A
M
+
∠
M
C
B
=
9
0
o
\angle CAM + \angle MCB = 90^o
∠
C
A
M
+
∠
MCB
=
9
0
o
, show that triangle
A
B
C
ABC
A
BC
is isosceles or right.
geometry
right triangle
isosceles
angles
midpoint