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1954 AMC 12 Question 35

AMC12 · 1954 AMC 12

Question 35

In the right triangle shown the sum of the distances $\overline{BM}$ and $\overline{MA}$ is equal to the sum of the distances $\overline{BC}$ and $\overline{CA}.$ If $\overline{MB}=x,$ $\overline{CB}=h,$ and $\overline{CA}=d,$ then $x$ equals:

Question illustration
  1. $\dfrac{hd}{2h+d}$
  2. $d-h$
  3. $\dfrac12d$
  4. $h+d-\sqrt{2d}$
  5. $\sqrt{h^2+d^2}-h$