MathDB
Obtuse triangle

Source:

October 24, 2005
geometrytrigonometry

Problem Statement

In the obtuse triangle ABCABC, AM=MB,MDBC,ECBCAM = MB, MD \perp BC, EC \perp BC. If the area of ABC\triangle ABC is 24, then the area of BED\triangle BED is
[asy] size(200); defaultpen(linewidth(0.8)+fontsize(11pt)); pair A = (6.5,3.2), B = origin, C = (5.0), D = (3.3,0); pair Xc = (C.x,4), Xd = (D.x,4), E = intersectionpoint(A--B,C--Xc), M = intersectionpoint(D--Xd, A--B); draw(C--A--B--C--E--D--M); label("AA",A,NE); label("BB",B,W); label("CC",C,SE); label("DD",D,S); label("EE",E,N); label("MM",M,N); draw(rightanglemark(D,C,E,7)^^rightanglemark(B,D,M,7)); [/asy]
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>12<spanclass=latexbold>(C)</span>15<spanclass=latexbold>(D)</span>18<spanclass=latexbold>(E)</span>not uniquely determined<span class='latex-bold'>(A) </span>9\qquad <span class='latex-bold'>(B) </span>12\qquad <span class='latex-bold'>(C) </span>15\qquad <span class='latex-bold'>(D) </span>18\qquad <span class='latex-bold'>(E) </span>\text{not uniquely determined}