Two nested right triangles with their incircles. Two tangency points are shown. Prove that the red and yellow line segments are parallel.

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## Solution

The argument is that triangle ABC with its incircle is similar to triangle BDC with its incircle. This implies that |CE| : |CB| = |CF| : |CD|, which, by the converse of the Triangle proportionality theorem, ensures that BD // EF.

## Video

Please find here the video solution: Video: The doubleganger.