Calculating the area of overlap between 2 circle sectors

E

evansba

New member
Joined
Mar 18, 2019
Messages
4
Is it possible to calculate the area of overlap between 2 circle sectors based on:

- The distance between the centres of each sector
- The length of the sector (radius)
- The interior angle of the sector
- The angle that the sector has been rotated off a reference line assuming that this reference line is the line travelling horizontally through the centre of a circle (as seen in diagram B with the sector being rotated by 60 degrees off the origin)

Diagram A showcases an exemplar sector that I am referring to and diagram C showcases the combination of 2 sectors rotated at different angles and positioned 3 units apart, with both having the same interior angle and the same radius length

I'm not sure this is even possible, but hoping it is, so any help would be greatly appreciated
 

Attachments

  • Screenshot_20240326-180413_Samsung Notes.jpg
    Screenshot_20240326-180413_Samsung Notes.jpg
    269.4 KB · Views: 14
evansba said:
Is it possible to calculate the area of overlap between 2 circle sectors based on:

- The distance between the centres of each sector
- The length of the sector (radius)
- The interior angle of the sector
- The angle that the sector has been rotated off a reference line assuming that this reference line is the line travelling horizontally through the centre of a circle (as seen in diagram B with the sector being rotated by 60 degrees off the origin)

Diagram A showcases an exemplar sector that I am referring to and diagram C showcases the combination of 2 sectors rotated at different angles and positioned 3 units apart, with both having the same interior angle and the same radius length

I'm not sure this is even possible, but hoping it is, so any help would be greatly appreciated
Click to expand...
I think it's possible. Is this a school assignment?
 
First, with a more accurate diagram, we see that you can approximate the area easily, as a mere sector:

1711546490996.png​

So you may not really need an accurate calculation.

But if you want an exact formula (illustrated here with different numbers), I would add in these extra lines and work out areas of sectors and triangles to combine to get the desired area:

1711547882638.png​
 
You must log in or register to reply here.
Top