Right Triangle
Source:
February 7, 2009
Problem Statement
In the right triangle shown the sum of the distances and is equal to the sum of the distances and . If MB \equal{} x, CB \equal{} h, and CA \equal{} d, then equals:
[asy]size(200); defaultpen(linewidth(.8pt)+fontsize(10pt));
dotfactor=4;
draw((0,0)--(8,0)--(0,5)--cycle);
label("C",(0,0),SW);
label("A",(8,0),SE);
label("M",(0,5),N);
dot((0,3.5));
label("B",(0,3.5),W);
label("",(0,4.25),W);
label("",(0,1),W);
label("",(4,0),S);[/asy] (A)\ \frac {hd}{2h \plus{} d} \qquad (B)\ d \minus{} h \qquad (C)\ \frac {1}{2}d \qquad (D)\ h \plus{} d \minus{} \sqrt {2d} \qquad (E)\ \sqrt {h^2 \plus{} d^2} \minus{} h