3. Given the radius of $\odot O$ is 10, the distance from point $P$ to the center $O$ is 8, the number of chords passing through point $P$ and having integer lengths is ( ) .
(A) 16
(B) 14
(C) 12
(D) 9
3. (A).

The diameter passing through point $P$ is 20 units long, and the chord passing through point $P$ and perpendicular to the diameter is between 12.12 and 20 units long. There are 7 more integer values between 12.12 and 20, considering the symmetry, the number of chords sought is $2+7 \times 2=16$.