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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
10
10
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR 2019 P10
Source:
3/6/2019
Let
N
N
N
be the midpoint of arc
A
B
C
ABC
A
BC
of the circumcircle of
Δ
A
B
C
\Delta ABC
Δ
A
BC
, and
N
P
NP
NP
,
N
T
NT
NT
be the tangents to the incircle of this triangle. The lines
B
P
BP
BP
and
B
T
BT
BT
meet the circumcircle for the second time at points
P
1
P_1
P
1
and
T
1
T_1
T
1
respectively. Prove that
P
P
1
=
T
T
1
PP_1 = TT_1
P
P
1
=
T
T
1
.
geometry