MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
2018 Canada National Olympiad
2
2
Part of
2018 Canada National Olympiad
Problems
(1)
Five points [CMO 2018 - P2]
Source: 2018 Canadian Mathematical Olympiad - P2
3/31/2018
Let five points on a circle be labelled
A
,
B
,
C
,
D
A, B, C, D
A
,
B
,
C
,
D
, and
E
E
E
in clockwise order. Assume
A
E
=
D
E
AE = DE
A
E
=
D
E
and let
P
P
P
be the intersection of
A
C
AC
A
C
and
B
D
BD
B
D
. Let
Q
Q
Q
be the point on the line through
A
A
A
and
B
B
B
such that
A
A
A
is between
B
B
B
and
Q
Q
Q
and
A
Q
=
D
P
AQ = DP
A
Q
=
D
P
Similarly, let
R
R
R
be the point on the line through
C
C
C
and
D
D
D
such that
D
D
D
is between
C
C
C
and
R
R
R
and
D
R
=
A
P
DR = AP
D
R
=
A
P
. Prove that
P
E
PE
PE
is perpendicular to
Q
R
QR
QR
.
geometry