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Canada National Olympiad
1986 Canada National Olympiad
3
3
Part of
1986 Canada National Olympiad
Problems
(1)
Constant chord implies constant angle
Source: Canadian Mathematical Olympiad - 1986 - Problem 3.
7/3/2011
A chord
S
T
ST
ST
of constant length slides around a semicircle with diameter
A
B
AB
A
B
.
M
M
M
is the midpoint of
S
T
ST
ST
and
P
P
P
is the foot of the perpendicular from
S
S
S
to
A
B
AB
A
B
. Prove that
∠
S
P
M
\angle SPM
∠
SPM
is constant for all positions of
S
T
ST
ST
.
geometry proposed
geometry