Triangle in triangle

Inscribe a given triangle into a given triangle. (Compass and straightedge construction)
That is the vertices of the smaller lie on each side of the larger (one vertex on each side).
Inspired by Zak Seidov Web site Pb #74 and #75

We start with a simple example :
Inscribe a given right angled triangle (say sides 3,4,5) into a given right angled triangle (say sides 5,12,13), the right angle of the smaller triangle being on the hypothenuse of the larger.
Solution

A little more complicated :
Find other locations where the right angle of the smaller lies on another side of the larger.
Hint

And then ... Study the general case, that is any triangle into any larger triangle   
Hint

Details

 

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