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Lines in a plane

Source: 1970 AHSME Problem 20

March 24, 2014
AMC

Problem Statement

Lines HKHK and BCBC lie in a plane. MM is the midpoint of line segment BCBC, and BHBH and CKCK are perpendicular to HKHK. Then we
<spanclass=′latex−bold′>(A)</span>always have MH=MK<spanclass=′latex−bold′>(B)</span>always have MH>BK<span class='latex-bold'>(A) </span>\text{always have }MH=MK\qquad<span class='latex-bold'>(B) </span>\text{always have }MH>BK\qquad
<spanclass=′latex−bold′>(C)</span>sometimes have MH=MK but not always<span class='latex-bold'>(C) </span>\text{sometimes have }MH=MK\text{ but not always}\qquad
<spanclass=′latex−bold′>(D)</span>always have MH>MB<spanclass=′latex−bold′>(E)</span>always have BH<BC<span class='latex-bold'>(D) </span>\text{always have }MH>MB\qquad <span class='latex-bold'>(E) </span>\text{always have }BH<BC
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