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JOM 2015 Shortlist
G8
G8
Part of
JOM 2015 Shortlist
Problems
(1)
Circumcircles tangent
Source: Junior Olympiad of Malaysia Shortlist 2015 G8
7/17/2015
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a convex pentagon such that
B
C
BC
BC
and
D
E
DE
D
E
are tangent to the circumcircle of
A
C
D
ACD
A
C
D
. Prove that if the circumcircles of
A
B
C
ABC
A
BC
and
A
D
E
ADE
A
D
E
intersect at the midpoint of
C
D
CD
C
D
, then the circumcircles
A
B
E
ABE
A
BE
and
A
C
D
ACD
A
C
D
are tangent to each other.
geometry
circumcircle