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International Contests
Nordic
1995 Nordic
1
1
Part of
1995 Nordic
Problems
(1)
equal segments from perpendiculars and a diameter
Source: Nordic Mathematical Contest 1995 #1
10/4/2017
Let
A
B
AB
A
B
be a diameter of a circle with centre
O
O
O
. We choose a point
C
C
C
on the circumference of the circle such that
O
C
OC
OC
and
A
B
AB
A
B
are perpendicular to each other. Let
P
P
P
be an arbitrary point on the (smaller) arc
B
C
BC
BC
and let the lines
C
P
CP
CP
and
A
B
AB
A
B
meet at
Q
Q
Q
. We choose
R
R
R
on
A
P
AP
A
P
so that
R
Q
RQ
RQ
and
A
B
AB
A
B
are perpendicular to each other. Show that
B
Q
=
Q
R
BQ =QR
BQ
=
QR
.
geometry
equal segments