3. As shown in the figure, $AB$ is the diameter of a semicircle, $O$ is the center of the circle, $CD \perp AB, DE \perp OC$. If the lengths of $AD, BD$, and $CD$ are all rational numbers, then
Proposition
甲、The length of $OE$ is a rational number;

乙、The length of $DE$ is a rational number;

丙、The lengths of all line segments marked with letters in the figure are rational numbers.
(A) Only 甲 is correct; (B) Only 乙 is correct;
(C) Only 甲 and 乙 are correct;
(D) 甲, 乙, and 丙 are all correct.