BdMO National Junior 2007/5

[samiul_samin]

Find the difference between the non shaded area ($ABDF$ & $FCE$) of thre triangles.Instead of triangles,if there were circles or any other shape,what would be the result -comment on that.

Screenshot_2019-02-24-10-46-54-1.png

[samiul_samin]

Let, $[x]$ denote area of $x$
From the diagram
\[[ACD]=[ABDF]+[BFC]...(i)\].
\[[BCE]=[FCE]+[BFC]...(ii)\]

$(i)-(ii)$,

\[[ABDF]-[FCE]=[ACD]-[BCE]\]
It would be same for any shape.Diagramatic example for
$Circle:$

Screenshot_2019-02-24-15-09-53-1.png

$Square$

Screenshot_2019-02-24-15-10-48-1.png