The nine-point circle of a triangle is a circle that passes through nine significant points:

• The midpoint of each side of the triangle

• The foot of each altitude

• The midpoint of the segment that join the vertex and the orthocenter.

Orthocenter is the concurrent point of the altitudes of a triangle.
Internally tangent circles: intersecting at exactly one point, with one circle inside the other
Externally tangent circles: intersecting at exactly one point, with neither circle inside the other.
Incircle or inscribed circle: a circle that is tangent to each of the triangle's three sides
Excircle or escribed circle: a circle tangent to one side of the triangle and to the extensions of the other sides.
 

Dynamic Geometry: You can alter the figure above dynamically in order to test and prove (or disproved) conjectures and gain mathematical insight that is less readily available with static drawings by hand.

This page uses the TracenPoche dynamic geometry software and requires Adobe Flash player 7 or higher. TracenPoche is a project of Sesamath, an association of French teachers of mathematics.

Instruction to explore the illustration above:

• Animation. Click the red button to start/stop animation

• Manipulate. Drag points A and C, and line AC to change the figure.

• Step-by-Step construction. Press P and click the left mouse button on any free area to show the step-by-step bar and click 'Next Step' button () to start the construction step-by-step:
   
  Hide the step-by-step bar by using again the combination P + click left mouse.