Final answer:
After finding that BE and EC are equal due to DE being a perpendicular bisector, we deduce that OC = 9 centimeters and BC = 8 centimeters, none of which match the provided options. There might be an error in the question or options.
Step-by-step explanation:
In triangle ABC, DE is the perpendicular bisector of side BC, which means DE splits BC into two equal lengths and forms a 90-degree angle with BC. Given that OB = 5 centimeters and BE = 4 centimeters, we know that since DE is a bisector, EB = EC. Therefore, if EB is 4 centimeters, then EC must also be 4 centimeters, because a perpendicular bisector creates two equal halves. So, OC, which is the sum of OB and BC, is 5 cm (OB) + 4 cm (BE) = 9 cm. However, there seems to be a mistake in the presented options.
Then, from OC we can find the length of side BC by adding the lengths BE and EC together, which gives us BC = 4 cm (BE) + 4 cm (EC) = 8 cm. So, it appears that none of the provided choices correctly match the calculations based on the given information. There may be a typo in the question or the provided options.