The point is the symmedian point of the orthic triangle (shown in red) of [1].

Let

, , be the side lengths,

, , be the circumradius, inradius and semiperimeter of ,

,

, , be the exact trilinear coordinates of with respect to and .

Then, with

,

we have

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da=FractionBox[RowBox[{"S", RowBox[{"(", RowBox[{RowBox[{"b", " ", "c", " ", "S"}], "+", RowBox[{"a", " ", "R", RowBox[{"(", RowBox[{RowBox[{"4", SuperscriptBox["R", "2"]}], "-", RowBox[{"2", SubscriptBox["S", "A"]}], "-", SubscriptBox["S", "ω"]}], ")"}]}]}], ")"}]}], RowBox[{"2", "R", " ", "f"}]],

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You can drag the vertices , , .