Mandart’s inellipse is tangent to each side of the triangle that contains it and its center is the mittenpunkt, which is the point that results from the intersection of the lines that leave the
vertices of the triangle formed by the centers of the circumferences exinscribed to the original triangle and that pass through each of its midpoints. The Nagel point is added in this version, which is the
intersection point of the lines that go from each tangent point of the exinscribed circles to the opposite vertex of the triangle that contains the Mandart inellipse.
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There is a WFR function handles generic inellipse:
https://resources.wolframcloud.com/FunctionRepository/resources/Inellipse/
Mandart inellipse is in the neat example section.
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Thanks!! I know about that function in resources, but sometimes I prefer create things by me.
But thank you Ph.D Yang!!