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Home » The radius $r$ of the incircle of a right triangle is given by: - SUpost

The radius $r$ of the incircle of a right triangle is given by: - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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u^2 + 1 = 3u \quad \Rightarrow \quad u^2 - 3u + 1 = 0.
u = rac{3 \pm \sqrt{9 - 4}}{2} = rac{3 \pm \sqrt{5}}{2}.
So \( u = rac{3 + \sqrt{5}}{2} \) or \( u = rac{3 - \sqrt{5}}{2} \).
Now recall \( u = rac{x+y}{x-y} \). Let \( r = rac{x}{y} \), assumin...
e 0\). Then:
rac{x+y}{x-y} = rac{r+1}{r-1}.
Set this equal to each value of \(u\):
Case 1:** \( rac{r+1}{r-1} = rac{3 + \sqrt{5}}{2} \)
2(r+1) = (3 + \sqrt{5})(r - 1)
2r + 2 = (3 + \sqrt{5})r - (3 + \sqrt{5})

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