To find the length of the minor arc corresponding to a central angle of 90 degrees in a circle with a circumference of \( 20\pi \), we can use the formula for the length of an arc. The length of an arc \( L \) can be calculated using the formula:
\[ L = \frac{\theta}{360^\circ} \times C \]
where:
- \( \theta \) is the central angle in degrees,
- \( C \) is the circumference of the circle.
In this case:
- \( \theta = 90^\circ \)
- \( C = 20\pi \)
Now plug in the values:
\[ L = \frac{90}{360} \times 20\pi \]
First, simplify \( \frac{90}{360} \):
\[ \frac{90}{360} = \frac{1}{4} \]
Now substitute this back into the equation:
\[ L = \frac{1}{4} \times 20\pi = 5\pi \]
Thus, the length of the minor arc is
\[ \boxed{5\pi} \]
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