Seeing double II

A right triangle is divided in two triangles by an altitude. The three incircles are shown with three tangency points. Prove that the two red line segments are congruent.

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Solution by VIVEK.

Note that this solution does not use the right angles, so the congruence is valid for any triangle and cevian.

General version of this puzzle.


Please find here the video solution: Video: Seeing double II.

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