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Baltic Way
1990 Baltic Way
8
8
Part of
1990 Baltic Way
Problems
(1)
Simson lines of opposite points are perpendicular
Source:
4/19/2013
It is known that for any point
P
P
P
on the circumcircle of a triangle
A
B
C
ABC
A
BC
, the orthogonal projections of
P
P
P
onto
A
B
,
B
C
,
C
A
AB,BC,CA
A
B
,
BC
,
C
A
lie on a line, called a Simson line of
P
P
P
. Show that the Simson lines of two diametrically opposite points
P
1
P_1
P
1
and
P
2
P_2
P
2
are perpendicular.
geometry
circumcircle