Incircle
The incenter (I) of a triangle is the point on the interior oof the triangle that is equidstant from the three sides. Since a point interior to an angle is equidistant from the two sides of the angle lies on the angle bisector, then I must be on the angle bisector of each angle of the triangle.
The inscribed circle of the triangle is called the INCIRCLE. The center of this circle is I .

Notice that the point where all three of the angle bisectors intersect the opposite sides of the triangle lie on the circle.

Click here for a GSP script to consruct the incircle given any three points (the verticies of a triangle).

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Triangles

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