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[Community Question] Geometry: Find the radius of the circle drawn inside the triangle.

One of our user asked:

enter image description here

Let, the point $K$ is the radius of the circle drawn inside the triangle.

$\angle ABC=90°$

$AE=4$ and $CF=12$

The problem is, to find the radius of the circle drawn inside the triangle.

My attempt.

The formula for $r$, we have

$r=\frac{2A}{a+b+c}$, where $A$, is area of Triangle. So, I need, $a,b,c$. It is obvious, $c=\sqrt{a^2+b^2}$. Then, I need $AB$ and $BC$. Or, I must know what are $BE$ and $BF$. I 'm stuck..


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