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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2021 Sharygin Geometry Olympiad
10-11.3
10-11.3
Part of
2021 Sharygin Geometry Olympiad
Problems
(1)
cyclic wanted, circumcircle and another circle related
Source: 2021 Sharygin Finals grades X-XI p3
8/1/2021
The bisector of angle
A
A
A
of triangle
A
B
C
ABC
A
BC
(
A
B
>
A
C
AB > AC
A
B
>
A
C
) meets its circumcircle at point
P
P
P
. The perpendicular to
A
C
AC
A
C
from
C
C
C
meets the bisector of angle
A
A
A
at point
K
K
K
. A cừcle with center
P
P
P
and radius
P
K
PK
P
K
meets the minor arc
P
A
PA
P
A
of the circumcircle at point
D
D
D
. Prove that the quadrilateral
A
B
D
C
ABDC
A
B
D
C
is circumscribed.
geometry
Concyclic
Cyclic