An Inequality Relating the Nagel Point and Exact Trilinear Coordinates
Given a triangle , let be the circumcenter and be the Nagel point. (See the MathWorld related link for the definition of the Nagel point.)[more]
For a point , the vertices of the pedal triangle of with respect to are the feet of the perpendiculars from to the sides of .
Let , , be the exact trilinear coordinates of with respect to the sides , , and let .
Let , be the circumradius and inradius of and let .
You can drag the points , , and .[less]