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Adygea Teachers' Geometry Olympiad
2021 Adygea Teachers' Geometry Olympiad
3
3
Part of
2021 Adygea Teachers' Geometry Olympiad
Problems
(1)
equal segments by excircles (2021 Adygea Teachers' Geometry Olympiad p3)
Source:
3/31/2021
In a triangle, one excircle touches side
A
B
AB
A
B
at point
C
1
C_1
C
1
and the other touches side
B
C
BC
BC
at point
A
1
A_1
A
1
. Prove that on the straight line
A
1
C
1
A_1C_1
A
1
C
1
the constructed excircles cut out equal segments.
geometry
excircle