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 .

**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.

© 1996-9

1999-05-25