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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2022 Sharygin Geometry Olympiad
9.4
9.4
Part of
2022 Sharygin Geometry Olympiad
Problems
(1)
Lines intersect on angle bisector
Source: Sharygin Finals 2022 9.4
8/1/2022
Let
A
B
C
ABC
A
BC
be an isosceles triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
,
P
P
P
be the midpoint of the minor arc
A
B
AB
A
B
of its circumcircle, and
Q
Q
Q
be the midpoint of
A
C
AC
A
C
. A circumcircle of triangle
A
P
Q
APQ
A
PQ
centered at
O
O
O
meets
A
B
AB
A
B
for the second time at point
K
K
K
. Prove that lines
P
O
PO
PO
and
K
Q
KQ
K
Q
meet on the bisector of angle
A
B
C
ABC
A
BC
.
geometry
angle bisector