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Area Question

2 circles, each of radius r, overlap each other and the centre of one circle is the circumference of the other circle. Show that the area of overlap is r^2/4(4pi-3root3).

How would I go about this? I have no idea where to start lol


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Reply 1
Avatar for Notnek
Notnek
21
Original post by Mr Pussyfoot
2 circles, each of radius r, overlap each other and the centre of one circle is the circumference of the other circle. Show that the area of overlap is r^2/4(4pi-3root3).

How would I go about this? I have no idea where to start lol


Posted from TSR Mobile

Hint : try to form sectors of radius rr in the overlapping region.

The denominator of the answer is 66 not 44 so the answer is

r26(4π−33)\displaystyle \frac{r^2}{6}\left(4\pi-3\sqrt{3}\right)
(edited 7 years ago)
Reply 2
Avatar for MartyO
MartyO
7

Spoiler

Reply 3
Avatar for Zacken
Zacken
22
Original post by MartyO
...


Heya! I see that you've been answering a few threads as of late, just thought that I'd let you know that here on TSR, we prefer to guide users and refrain from posting full solutions to queries, instead, that is left as a last ditch resort. Indeed, given that notnek posted a hint, it comes off as a bit rude for you to post a full solution. Thanks for reading and understanding! :-)
Reply 4
Avatar for Mr Pussyfoot
Mr Pussyfoot
OP
Original post by notnek
Hint : try to form sectors of radius rr in the overlapping region.

The denominator of the answer is 66 not 44 so the answer is

r26(4π−33)\displaystyle \frac{r^2}{6}\left(4\pi-3\sqrt{3}\right)


Thanks! I had trouble visualising it at first but the hint really helped. And yes it is r^2/6 (my mistake lol)


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Reply 5
Avatar for Mr Pussyfoot
Mr Pussyfoot
OP
Original post by MartyO

Spoiler



I think this method is a little too advanced for someone at my level!😂 But never would have imagined the problem could be approached in this way


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