Diagram: Construct Circle w/ 9 Equal Parts

[Albert1]

divide a circle into 9 parts with equal area

 

[Albert1]

divide a circle into 9 parts with equal area

my solution:

Spoiler

construct two circles with the same center $O$
the bigger circle with radius $9k$
the smaller circle with radius $3k$
$(k>0)$
$A=$ the area inside and on the big circle
$B=$ the area inside and on the small circle=$\dfrac {A}{9}$
$C=$( the area inside $A$ and ouside $B)$=$\dfrac {8A}{9}=A-B$
divide $C$ into eight parts with equal area
each part will have area $\dfrac {8A}{9}\times \dfrac {1}{8}=\dfrac {A}{9}$=area of $B$