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Sharygin Geometry Olympiad
2023 Sharygin Geometry Olympiad
9.4
9.4
Part of
2023 Sharygin Geometry Olympiad
Problems
(1)
prove AIP and omega cut off equal chords on AD
Source: Sharygin Finals 2023 9.4
8/2/2023
The incircle
ω
\omega
ω
of a triangle
A
B
C
ABC
A
BC
centered at
I
I
I
touches
B
C
BC
BC
at point
D
D
D
. Let
P
P
P
be the projection of the orthocenter of
A
B
C
ABC
A
BC
to the median from
A
A
A
. Prove that the circle
A
I
P
AIP
A
I
P
and
ω
\omega
ω
cut off equal chords on
A
D
AD
A
D
.
geometry
Sharygin Geometry Olympiad
Sharygin 2023