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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 3
2019 Nigerian Senior MO Round 3
1
1
Part of
2019 Nigerian Senior MO Round 3
Problems
(1)
Cyclic quadrilaterals
Source: Nigeria MO 3rd round 2019 problem 1
9/8/2019
Let the altitude from
A
A
A
and
B
B
B
of triangle
A
B
C
ABC
A
BC
meet the circumcircle of
A
B
C
ABC
A
BC
again at
D
D
D
and
E
E
E
respectively. Let
D
E
DE
D
E
meet
A
C
AC
A
C
and
B
C
BC
BC
at
P
P
P
and
Q
Q
Q
respectively. Show that
A
B
Q
P
ABQP
A
BQP
is cyclic
geometry
cyclic quadrilateral