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2019 Pan-African
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PAMO Problem 4: Perpendicular lines
Source: 2019 Pan-African Mathematics Olympiad, Problem 4
4/9/2019
The tangents to the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
at
B
B
B
and
C
C
C
meet at
D
D
D
. The circumcircle of
△
B
C
D
\triangle BCD
△
BC
D
meets sides
A
C
AC
A
C
and
A
B
AB
A
B
again at
E
E
E
and
F
F
F
respectively. Let
O
O
O
be the circumcentre of
△
A
B
C
\triangle ABC
△
A
BC
. Show that
A
O
AO
A
O
is perpendicular to
E
F
EF
EF
.
geometry
PAMO
circumcircle