2000 PMWC Problems/Problem I13
Revision as of 16:38, 20 April 2014 by TheMaskedMagician (talk | contribs) (Created page with "==Problem== In the figure, the squares <math>ABCD</math> and <math>DCEG</math> both have the same area of <math>64cm^2</math>. <math>EFG</math> is a semicircle. The point <math>F...")
Problem
In the figure, the squares 
and 
both have the same area of 
. 
is a semicircle. The point 
is the mid-point of the arc . Find the area of the shaded part. (Assume 
)
![[asy] void unitsquare(pair p){ draw(p--(p.x+1,p.y)--(p.x+1,p.y+1)--(p.x,p.y+1)--cycle); return; } fill(buildcycle(arc((2,0.5),(2,0),(2,1)),(2,1)--(0,1)--(2.5,0.5)),gray); unitsquare((0,0)); draw((1,0)--(2,0)--(2,1)--(1,1)); draw(arc((2,0.5),(2,0),(2,1))); label("$A$",(0,1),NW); label("$B$",(0,0),SW); label("$C$",(1,0),S); label("$D$",(1,1),N); label("$E$",(2,0),S); label("$F$",(2.5,0.5),E); label("$G$",(2,1),N); //Credit to chezbgone2 for the diagram[/asy]](http://latex.artofproblemsolving.com/4/8/f/48fbdb9ab948aa92a7aa6061eefbedb0e0a04382.png)
