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Tournament Of Towns
1990 Tournament Of Towns
(268) 2
(268) 2
Part of
1990 Tournament Of Towns
Problems
(1)
TOT 268 1990 Autumn A J2 locus of midpoints, semicircle
Source:
6/8/2024
A semicircle
S
S
S
is drawn on
A
B
AB
A
B
as diameter. For an arbitrary point
C
C
C
in
S
S
S
(
C
≠
A
C\ne A
C
=
A
,
C
≠
B
C \ne B
C
=
B
), squares are attached to sides
A
C
AC
A
C
and
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
outside the triangle. Find the locus of the midpoint of the segment joining the centres of the squares as
C
C
C
moves along
S
S
S
.(J Tabov, Sofia)
geometry
Locus
semicircle