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ANSWER: 25.

EXPLANATION: Begin by labeling the diagram: We can form two equations:

1) 2a = r + h
2) a² + h² = r²

Isolating for h and replacing a with 10 yields:

1) h = 20 - r
2) h² = r² - 100

Transform the first equation into h² = (20 - r)²

Now we have:

(20 - r)² = r² - 100
400 + 2² -40r = r² - 100
40r = 500
r = 12.5

The diameter of the circle is therefore 25 cm.

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