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Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
19
19
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR 2019 P19
Source: Sharygin CR 2019 P19 (Grade 10 - 11)
3/6/2019
Let
A
L
a
AL_a
A
L
a
,
B
L
b
BL_b
B
L
b
,
C
L
c
CL_c
C
L
c
be the bisecors of triangle
A
B
C
ABC
A
BC
. The tangents to the circumcircle of
A
B
C
ABC
A
BC
at
B
B
B
and
C
C
C
meet at point
K
a
K_a
K
a
, points
K
b
K_b
K
b
,
K
c
K_c
K
c
are defined similarly. Prove that the lines
K
a
L
a
K_aL_a
K
a
L
a
,
K
b
L
b
K_bL_b
K
b
L
b
and
K
c
L
c
K_cL_c
K
c
L
c
concur.
geometry