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Swedish Mathematical Competition
2006 Swedish Mathematical Competition
2
2
Part of
2006 Swedish Mathematical Competition
Problems
(1)
Intouch triangle is acute
Source: 2006 Swedish Mathematical Competition #2
1/5/2018
In a triangle
A
B
C
ABC
A
BC
, point
P
P
P
is the incenter and
A
′
A'
A
′
,
B
′
B'
B
′
,
C
′
C'
C
′
its orthogonal projections on
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
, respectively. Show that
∠
B
′
A
′
C
′
\angle B'A'C'
∠
B
′
A
′
C
′
is acute.
geometry
incenter
Sweden