Incircle of a Triangle

The sketch below shows a circle inscribed in a triangle. Drag the vertices of the triangle around to see how they effect the inscribed circle. The circle is called the incircle of a triangle. The center of the incircle is the intersection of the angle bisectors of the triangle.

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The following are equivalent:
Angle Bisectors all meet
There is a point equidistant from all sides
There is an incircle

Michael Smith, July 17, 2008, Created with GeoGebra