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Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
9.1
9.1
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Excircles produce homothetic lines
Source: Sharygin Finals 2022 9.1
7/31/2022
Let
B
H
BH
B
H
be an altitude of right angled triangle
A
B
C
ABC
A
BC
(
∠
B
=
9
0
o
\angle B = 90^o
∠
B
=
9
0
o
). An excircle of triangle
A
B
H
ABH
A
B
H
opposite to
B
B
B
touches
A
B
AB
A
B
at point
A
1
A_1
A
1
; a point
C
1
C_1
C
1
is defined similarly. Prove that
A
C
/
/
A
1
C
1
AC // A_1C_1
A
C
//
A
1
C
1
.
geometry