MathDB

35

Part of 1954 AMC 12/AHSME

Problems(1)

Right Triangle

Source:

2/7/2009
In the right triangle shown the sum of the distances BM BM and MA MA is equal to the sum of the distances BC BC and CA CA. If MB \equal{} x, CB \equal{} h, and CA \equal{} d, then x x 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("xx",(0,4.25),W); label("hh",(0,1),W); label("dd",(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