To solve the problem, follow these steps:

Step 1: Identify key values

• AB is the diameter of circle O, so radius (OA = OB = OC = \frac{AB}{2} = 5) (since (AB = 10)).
• CD is a chord perpendicular to AB at E. By the theorem, the perpendicular from the center to a chord bisects the chord, so (CE = \frac{CD}{2} = 4) (since (CD = 8)).

Step 2: Use the Pythagorean theorem

△OEC is a right triangle (∠OEC = 90°). Applying Pythagoras:
[OC^2 = OE^2 + CE^2]

Substitute (OC = 5) and (CE = 4):
[5^2 = OE^2 + 4^2]
[25 = OE^2 + 16]
[OE^2 = 25 - 16 = 9]
[OE = 3]

Answer: (\boxed{3})

作者声明:本文包含人工智能生成内容。