South African Mathematics Olympiad First Round

$OABC$ is a rectangle of length $16$ cm. $M$ is the midpoint of $CB$ and $P$ lies on $AB$ so that $BP=3$ cm. The length $OM$ is $17$ cm. The length of $OP$, in cm, is (A) $18$ (B) $19$ (C) $20$ (D) $21$ (E) $22$