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1982 Brazil National Olympiad
1
1
Part of
1982 Brazil National Olympiad
Problems
(1)
triangle of incenter and 2 excenters is similar to original triangle
Source: Brazilian Mathematical Olympiad 1982 P1
7/27/2018
The angles of the triangle
A
B
C
ABC
A
BC
satisfy
∠
A
/
∠
C
=
∠
B
/
∠
A
=
2
\angle A / \angle C = \angle B / \angle A = 2
∠
A
/∠
C
=
∠
B
/∠
A
=
2
. The incenter is
O
.
K
,
L
O. K, L
O
.
K
,
L
are the excenters of the excircles opposite
B
B
B
and
A
A
A
respectively. Show that triangles
A
B
C
ABC
A
BC
and
O
K
L
OKL
O
K
L
are similar.
geometry
incenter
excenters
similar triangles