1970 AHSME Problem 20

Lines HK and BC lie in a plane. M is the midpoint of line segment BC, and BH and CK are perpendicular to HK. Then we

\begin{array}{l} \textbf{(A) }\text{always have }MH=MK\qquad\\ \textbf{(B) }\text{always have }MH>BK\qquad\\ \textbf{(C) }\text{sometimes have }MH=MK\text{ but not always}\qquad\\ \textbf{(D) }\text{always have }MH>MB\qquad \\ \textbf{(E) }\text{always have }BH<BC \end{array}

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