10217

# The Second Lemoine Circle

Through the symmedian point K of a triangle ABC draw lines parallel to the sides of the orthic triangle. The six points of intersection of those lines with the sides of the triangle lie on a circle (the second Lemoine circle) with center K.

### DETAILS

The triangle formed by the intersection of the altitudes with the sides of a triangle ABC is called the orthic triangle of ABC.
The centroid of a triangle is the intersection of the lines drawn from the vertices to the midpoints of the opposite sides.
Let P be a point inside ABC. The reflections of the three lines AP, BP, and CP in the angle bisectors at A, B, and C meet in a point, called the isogonal conjugate of P.
The symmedian point is the isogonal conjugate of a triangle's centroid.

### PERMANENT CITATION

Contributed by: Jay Warendorff
After work by: Paul Yiu
 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.