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Spain Mathematical Olympiad
2020 Spain Mathematical Olympiad
5
5
Part of
2020 Spain Mathematical Olympiad
Problems
(1)
AC+BC = sqrt(2)AB -> O(BMP) tangent to AC.
Source: Spain Mathematical Olympiad 2020 P5
7/15/2020
In an acute-angled triangle
A
B
C
ABC
A
BC
, let
M
M
M
be the midpoint of
A
B
AB
A
B
and
P
P
P
the foot of the altitude to
B
C
BC
BC
. Prove that if
A
C
+
B
C
=
2
A
B
AC+BC = \sqrt{2}AB
A
C
+
BC
=
2
A
B
, then the circumcircle of triangle
B
M
P
BMP
BMP
is tangent to
A
C
AC
A
C
.
geometry
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