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[Community Question] Geometry: How can I find the radius of inscribed circle of a triangle?

One of our user asked:

1

Let, the point $K$ is the center of inscribed circle of a triangle. The circle touching the edges of the triangle is mentioned.

$\angle ABC=90°$

$AE=4$ and $CF=12$

Find the radius of inscribed circle of the triangle:

A)3

B)4

C)5

D)6

E)7

My attempts:

The radius of inscribed circle, we have,

$r=\frac{a+b-c}{2}$, where, $c=\sqrt{a^2+b^2}$. Then, I need $AB$ and $BC$. Or, I must know what are $BE$ and $BF$. I 'm stuck.


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