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Old Kyiv MO Geometry
Kyiv City MO Seniors 2003+ geometry
2005.11.2
2005.11.2
Part of
Kyiv City MO Seniors 2003+ geometry
Problems
(1)
isosceles criterion with touchpoints with circle (Kyiv City Olympiad 2005 11.2)
Source:
6/27/2020
A circle touches the sides
A
C
AC
A
C
and
A
B
AB
A
B
of the triangle
A
B
C
ABC
A
BC
at the points
B
1
{{B}_ {1}}
B
1
and
C
1
{{C}_ {1}}
C
1
respectively. The segments
B
B
1
B {{B} _ {1}}
B
B
1
and
C
C
1
C {{C} _ {1}}
C
C
1
are equal. Prove that the triangle
A
B
C
ABC
A
BC
is isosceles. (Timoshkevich Taras)
geometry
isosceles
circle