Question asks to
Prove the diametre of a circle inscribed in a right angle triangle is equal to the sum of the two shorter sides minus that of the hypotheneus
I was able to create a diagram (like the one below) and attempted to create as many congruent triangles as I could with the right angle triangle's sides so I could find some way to prove them similar in some way to the radius but I have been unable to link them. Can you please help?
With the image ignore the numbers and listings they are irrelevant to the question. Just here as a reference
Best Answer
$AB = AF + FB$
$BC = BD + DC = FB + r$
$CA = CE + EA = r + AF$
$BC + CA = 2r + AF + FB = 2r + AB$
Diameter = $2r = BC + CA - AB$