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Home » We want to find the **maximum value of $r$** for which this equation has a solution. - Abbey Badges

We want to find the maximum value of $r$ for which this equation has a solution. - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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The area of a right triangle with inradius $ r $ and hypotenuse $ h $...
A_{\text{triangle}} = r \cdot \frac{a + b + h}{2}
But in a right triangle, the inradius is related to the sides $ a, b,...
r = \frac{a + b - h}{2}
Also, the area of the triangle is:
However, using the inradius formula, we can express the triangle’s are...
A_{\text{triangle}} = r \cdot s \quad \text{where } s = \frac{a + b +...
So the ratio becomes:
\frac{A_{\text{circle}}}{A_{\text{triangle}}} = \frac{\pi r^2}{r s} =...
Substituting $ s = \frac{a + b + h}{2} $, the final expression for the...

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