#### Answer

$\frac{m}{b} = \frac{b}{c}$

#### Work Step by Step

All three triangles are similar to one another, meaning that the sides of the triangles are proportional.
We can see that $b$ is the hypotenuse of the smaller triangle formed by the altitude of the large triangle. Additionally, $b$ is the shorter leg of the large triangle, and $c$ is the hypotenuse of the large triangle. What we want is the corresponding shorter leg in this smaller triangle, which is represented by $m$.
The proportion should read:
$\frac{m}{b} = \frac{b}{c}$