Given an arc PQ with curvature $\frac{1}{9}$
Three identical circles with radii 3 and centered at B,G,A respectively.
The circumference of the circles pass through each other's centers. Find the area of the shaded region. Would solving angle DHF be possible in this figure? So I could just get the area of the sector DHF and remove excess area. Any other solutions are very much welcome!
I am not really good with geometry and know only a few theorems. I would really appreciate if people could help me out here. Thank you for all your help!
Best Answer
If you know about polar coordinates (and especially equations of circles that are tangent to the origin) and you know about integration, then you could find these areas by placing the origin at $G$. You would make use of the radii ($3$ and $9$) to find the angles at which the $A$- and $B$-centered circles are oriented relative to your primary polar axis.