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Problems
Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2022 Philippine MO
6
6
Part of
2022 Philippine MO
Problems
(1)
Circumcircle tangency
Source: Philippine MO 2022/6
3/19/2022
In
△
A
B
C
\triangle ABC
△
A
BC
, let
D
D
D
be the point on side
B
C
BC
BC
such that
A
B
+
B
D
=
D
C
+
C
A
.
AB+BD=DC+CA.
A
B
+
B
D
=
D
C
+
C
A
.
The line
A
D
AD
A
D
intersects the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
again at point
X
≠
A
X \neq A
X
=
A
. Prove that one of the common tangents of the circumcircles of
△
B
D
X
\triangle BDX
△
B
D
X
and
△
C
D
X
\triangle CDX
△
C
D
X
is parallel to
B
C
BC
BC
.
geometry
circumcircle