nine-point circle
Triangle's special circle
In geometry, the nine-point circle is a circle that passes through nine significant points associated with any triangle: the midpoints of each side, the feet of each altitude, and the midpoints of the line segments from each vertex to the orthocenter.
Also called the Euler circle or Feuerbach circle, it demonstrates an elegant relationship between seemingly unrelated points in triangular geometry.
The nine-point circle's radius is always half that of the triangle's circumscribed circle.
- triangleThree-sided plane figure
- geometryScience of spatial relationships
- medialToward the body's center
- feetLower limbs' ends
- radiusCenter-to-perimeter distance
pedal · altitude · midpoint · geometric proofs · proofs · theorem · vertices · bisector · tangent · perpendicular · elegant · straightedge · Euclidean geometry · plane geometry · circumcenter · collinear · diameter · compass
- Trianglestriangle, equilateral, isosceles, scalene, right triangle
- circlesradius, circumference, pie chart, semicircle, ring
circle, nine, point, nineteenth, nonagon