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Also called the second Lemoine Circle. Draw lines through the Lemoine Point and Parallel to the
sides of the Triangles. The points where the antiparallel lines intersect the sides then lie on a
Circle known as the cosine circle with center at
. The Chords
,
, and
are proportional to the Cosines of the Angles of
, giving the circle
its name.
Triangles and
are directly similar, and
Triangles
and
are similar. The Miquel Point of
is at the Brocard Point
of
.
See also Brocard Points, Lemoine Circle, Miquel Point, Tucker Circles
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 271-273, 1929.