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Question: Why can neither solve nor SolveEquations find a correct inellipse?

Question:Why can neither solve nor SolveEquations find a correct inellipse?

Earl 955 Maple 2020
geometry solve rootfinding numeric directsearch ellipse
June 15 2021
1

In this worksheet the solve command almost immediately gives up and DirectSearch[SolveEquations] is erratic.

For some triangle/inellipse points of tangency the latter provides a nonsense answer and for others it produces an almost correct solution.

Is there a set of conditions which determine the possibility of an inellipse within a triangle?

Inellipse.mw

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