Incircle And Excircles Of A Triangle
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is called the triangle's incenter.
An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
The center of the incircle can be found as the intersection of the three internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle and the external bisectors of the other two. Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the incircle together with the three excircle centers form an orthocentric system.
See also Tangent lines to circles.
Read more about Incircle And Excircles Of A Triangle: Relation To Area of The Triangle, Nine-point Circle and Feuerbach Point, Gergonne Triangle and Point, Nagel Triangle and Point, Coordinates of The Incenter, Equations For Four Circles, Other Incircle Properties, Other Excircle Properties, Incircle in A Quadrilateral