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Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
22
22
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR P22
Source: Sharygin CR P22
3/6/2019
Let
A
A
0
AA_0
A
A
0
be the altitude of the isosceles triangle
A
B
C
(
A
B
=
A
C
)
ABC~(AB = AC)
A
BC
(
A
B
=
A
C
)
. A circle
γ
\gamma
γ
centered at the midpoint of
A
A
0
AA_0
A
A
0
touches
A
B
AB
A
B
and
A
C
AC
A
C
. Let
X
X
X
be an arbitrary point of line
B
C
BC
BC
. Prove that the tangents from
X
X
X
to
γ
\gamma
γ
cut congruent segments on lines
A
B
AB
A
B
and
A
C
AC
A
C
geometry