2002 AMC 12P Problem 8

Let AB be a segment of length 26, and let points C and D be located on AB such that AC=1 and AD=8. Let E and F be points on one of the semicircles with diameter AB for which EC and FD are perpendicular to AB. Find EF.

\text{(A) }5 \qquad \text{(B) }5 \sqrt{2} \qquad \text{(C) }7 \qquad \text{(D) }7 \sqrt{2} \qquad \text{(E) }12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.