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Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
14
14
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR 2019 P14
Source: Sharygin CR 2019 P14 (Grade 9 - 10)
3/6/2019
Let the side
A
C
AC
A
C
of triangle
A
B
C
ABC
A
BC
touch the incircle and the corresponding excircle at points
K
K
K
and
L
L
L
respectively. Let
P
P
P
be the projection of the incenter onto the perpendicular bisector of
A
C
AC
A
C
. It is known that the tangents to the circumcircle of triangle
B
K
L
BKL
B
K
L
at
K
K
K
and
L
L
L
meet on the circumcircle of
A
B
C
ABC
A
BC
. Prove that the lines
A
B
AB
A
B
and
B
C
BC
BC
touch the circumcircle of triangle
P
K
L
PKL
P
K
L
.
geometry