2018 AMC 10A Problem 16

Right triangle ABC has leg lengths AB=20 and BC=21. Including \overline{AB} and \overline{BC}, how many line segments with integer length can be drawn from vertex B to a point on hypotenuse \overline{AC}?

\textbf{(A) }5 \qquad \textbf{(B) }8 \qquad \textbf{(C) }12 \qquad \textbf{(D) }13 \qquad \textbf{(E) }15 \qquad

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