Triangles

Factual Questions
21

I explained how I derived the formula in post 15.

22

Thanks for reminding me. Could you fill in the missing steps that you indicated you left out?

23

a’ = a - x cot(beta) - x cot(gamma) - y csc(gamma) - z csc(beta)
= a - x (a^2+ c^2 - b^2)/(4A) - x (a^2+ b^2 - c^2)/(4A) - aby/(2A) - acz/(2A)
= a - a^2 x/(2A) - aby/(2A) - acz/(2A)
= a(A - ax/2 - by/2 - cz/2)/A

So…

A’ = A (a’/a)^2
= A ((A - ax/2 - by/2 - cz/)/A)^2)
= ((A - ax/2 - by/2 - cz/2)^2)/A

Keep in mind that I am posting from my phone so you may need to correct some typos here and there.