Wolfram Research

Mathematica MathWorld Wolfram Science More »

HOME

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.


	Contributed by: Jay Warendorff After work by: Paul Yiu

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.

"The Second Lemoine Circle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheSecondLemoineCircle/

Contributed by: Jay Warendorff

After work by: Paul Yiu

Report an issue »

Interact with Demonstrations using the latest version of the free Mathematica Player—Download Now

Browse all topics

	Source page:
	Email	Name (optional)
	Occupation (optional)	Organization (optional)
	I use Mathematica often occasionally never
	Country (optional) Remember me
	Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed. Privacy Policy »

Wolfram Research

Site Index

RSS

Atom