Let P be an internal point of the triangle ABC. Let the angle bisectors of the three angles from P to the vertices of ABC meet its sides at A', B', and C'.
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The Erdös-Mordell Inequality
A Triangle Inequality Involving the Altitudes, Semiperimeter, Inradius, and Circumradius
Perpendiculars from a Point on the Line between the Endpoints of the Angle Bisectors
The Area of the Incentral Triangle
Angle Bisector Theorem
The Intersection of an Angle Bisector and a Perpendicular Bisector
Division of an Angle Bisector by the Incenter
Two Triangles of Equal Area on Either Side of an Angle Bisector
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