

NinePoint Center, NinePoint Circle, Euler Line, Step by Step Interactive Illustration. Orthocenter, Circumcenter, Centroid, Midpoint.
HTML5 Animation. Click the Next button below to start.

The Ninepoint center is the center of
the ninepoint circle. The NinePoint Circle of triangle ABC
with orthocenter H is the circle that passes through the
feet of the altitudes H_{A}, H_{B} and H_{C} to the three sides, the
midpoints M_{A}, M_{B} and M_{C} of those sides, and the Euler Points
E_{A}, E_{B} and E_{C}, which are the midpoints of the segments AH, BH, and CH,
respectively. Euler line is the line passing through the
orthocenter H, the ninepoint center N, the
centroid G, and the
circumcenter O of any triangle ABC. Click the Next button
above to start the stepbystep illustration.

The ninepoint center N
is the midpoint of the line HO.

The distance from the
orthocenter H to the centroid G is twice the
distance from the circumcenter O to the centroid
G.

The ninepoint center N
is the circumcenter of the medial triangle M_{A}M_{B}M_{C}.

The ninepoint center N
is the circumcenter of the orthic triangle H_{A}H_{B}H_{C}.
The ninepoint circle is also known as
Euler's circle and Feuerbach's circle.
Leonhard Euler showed in 1765 that the
ninepoint circle bisects any line from the orthocenter to a
point on the circumcircle. In 1822
Karl Feuerbach discovered
that any triangle's ninepoint circle is externally tangent to
that triangle's three
excircles and internally tangent to its
incircle.


See Also:




NinePoint Center, NinePoint Circle, Euler Line, HTML5 Animation for iPad.
Circumcenter, Centroid, Orthocenter.


GeoGebra, Dynamic Geometry:
Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus) 

Geometry Problem 1361.
Triangle, Two NinePoint Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps. 

Geometry Problem 1360.
Triangle, NinePoint Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps. 

Geometry Problem
1062.
Scalene Triangle with an angle of 60 degrees, Euler Line, Orthocenter, Circumcenter, Distance, Congruence, Transversal. 

Geometry Problem 905: Lester Circle Theorem.


Geometry Problem 761
Scalene Triangle with an angle of 60 degrees, Euler Line, Equilateral Triangle. 

Circumcenter.
Index.


Centroid
/Barycenter.
Index.


Orthocenter
Index.


iPad Apps: Apollonius Software. Feuerbach Point. Triangle, Incircle, Nine point circle, Tangent circles, Orthocenter, Midpoint.
Interactive Geometry Software. 

Puzzle: Euler Line and Nine Point Center







