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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
15
15
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Sharygin 2022 P15
Source: Sharygin 2022
3/4/2022
A line
l
l
l
parallel to the side
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
touches its incircle and meets its circumcircle at points
D
D
D
and
E
E
E
. Let
I
I
I
be the incenter of
A
B
C
ABC
A
BC
. Prove that
A
I
2
=
A
D
ā
A
E
AI^2 = AD \cdot AE
A
I
2
=
A
D
ā
A
E
.
geometry
Sharygin Geometry Olympiad
Sharygin 2022
Inversion
similar triangles