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Contests
International Contests
Pan-African Shortlist
2019 Pan-African Shortlist
G3
G3
Part of
2019 Pan-African Shortlist
Problems
(1)
Line through intersection of diagonals of cyclic quad and mipoint of side
Source: 2019 Pan-African Shortlist - G3
1/18/2021
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral with its diagonals intersecting at
E
E
E
. Let
M
M
M
be the midpoint of
A
B
AB
A
B
. Suppose that
M
E
ME
ME
is perpendicular to
C
D
CD
C
D
. Show that either
A
C
AC
A
C
is perpendicular to
B
D
BD
B
D
, or
A
B
AB
A
B
is parallel to
C
D
CD
C
D
.
geometry
cyclic quadrilateral