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Tuymaada Olympiad
2017 Tuymaada Olympiad
2
2
Part of
2017 Tuymaada Olympiad
Problems
(1)
Geometrical inequality
Source: Tuymaada 2017 Junior Level
7/17/2017
A
B
C
D
ABCD
A
BC
D
is a cyclic quadrilateral such that the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
are perpendicular and their intersection is
P
P
P
. Point
Q
Q
Q
on the segment
C
P
CP
CP
is such that
C
Q
=
A
P
CQ=AP
CQ
=
A
P
. Prove that the perimeter of triangle
B
D
Q
BDQ
B
D
Q
is at least
2
A
C
2AC
2
A
C
.Tuymaada 2017 Q2 Juniors
geometry
inequalities