2006 AMC 10 #23
Source:
August 20, 2011
geometry
Problem Statement
A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 3, 7, and 7, as shown. What is the area of the shaded quadrilateral?
[asy]
unitsize(1.5cm);
defaultpen(.8);
pair A = (0,0), B = (3,0), C = (1.4, 2), D = B + 0.4*(C-B), Ep = A + 0.3*(C-A);
pair F = intersectionpoint( A--D, B--Ep );
draw( A -- B -- C -- cycle );
draw( A -- D );
draw( B -- Ep );
filldraw( D -- F -- Ep -- C -- cycle, mediumgray, black );
label("",(1.25,0.2));
label("",(2.2,0.45));
label("",(0.45,0.35));[/asy]