#### Answer

5.67 mm

#### Work Step by Step

We know that OE is 5 mm. In addition, since OE equals ED, and EF is half of ED, it follows that EF is half of 5, which is 2.5. Since OFE is a right angle, we use the Pythagorean theorem:
$OF^2 + 2.5^2 = 5^2 \\ OF = 4.33 mm$
Since OF plus FC equals 10, this means that FC equals $10 - 4.33 = 5.67$.