Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "Nine point circle"

 
Line 1: Line 1:
−
Also known as Euler's circle or Feuerbach's circle, as its name introduces itself that the nine point circle passes nine points, which are a given triangle <math>\triangle ABC</math>'s feet of altitude dropped from three vertices <math>A,B</math>, and <math>C</math>, usually denoted as <math>H_A,H_B,H_C</math>, and midpoints of three sides, as <math>M_A,M_B,M_C</math>, and three [[Euler point]]s <math>E_A,E_B,E_C</math>.
+
Also known as '''Euler's circle''' or '''Feuerbach's circle''', as its name introduces itself that the nine point [[circle]] goes through nine [[point]]s, which are a given [[triangle]] <math>\triangle ABC</math>'s feet of [[altitude]] dropped from three [[vertices]] <math>A,B</math>, and <math>C</math>, usually denoted as <math>H_A,H_B,H_C</math>, and [[midpoint]]s of three [[side]]s, as <math>M_A,M_B,M_C</math>, and three [[Euler point]]s <math>E_A,E_B,E_C</math>.

Revision as of 18:48, 4 November 2006

Also known as Euler's circle or Feuerbach's circle, as its name introduces itself that the nine point circle goes through nine points, which are a given triangle $\triangle ABC$'s feet of altitude dropped from three vertices $A,B$, and $C$, usually denoted as $H_A,H_B,H_C$, and midpoints of three sides, as $M_A,M_B,M_C$, and three Euler points $E_A,E_B,E_C$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Nine_point_circle&oldid=10855"