Formula for Common Area of Intersecting Circles

The area of a sector = R² * cos ¨¹ (R - H) - (R-H) √ 2Rh - H²

Where H = distance centre to x line - R.

add the same for r

After relaring h and H to the distance between centres.

That has to be a homework question...

hi

I used the wrong word, it should have been segment

the area of the sector (wedge) = 1/2 R²Θ = 1/2 R * s

where s = R Θ

and the A segment = A wedge/sector - A triangle

Thank You Mr. RAKESH SEMSEMWAL for your reply.

Indeed, I should have given the sketch. However in your sketch

what you have shown dimension x to be taken in a perpendicular

way to the line. i.e horizontal way and in this way value of x will be

smaller than what you have considered. In other words, the dimension

x shown in your sketch should be taken prpendicular way to the

line shown by you in your sketch. I hope now I have made my self clear.

DHAYANANDHAN.S'

CR4 MEMBER.

Mr.DHAYANANDHAN.S'

Thank you for your reply.

Equation still hold the validity with ref to the drawing I have made there, Only thing you will have to do is convert it to your desire.

If you feel any difficulty please don't hesitate and get back to me.

Thank you,

Regards.

Sorry Mr. . RAKESH SEMWAL,

While replying to your quiery, your name is wrongly typed.

Sincerely REGRET and apologise for the mistake.

dhayanandhan.s,

CR 4 MEMBER.

Hi dhayanandhan when you say:-

where x is the common ordinate for 2 circles.

what do you mean?

http://dictionary.die.net/ordinate

ordinate n : the value of a coordinate on the vertical axis

Maybe this:-

The point D has ordinate 2.64 which is less than (7-4).

Can you draw a picture of what you want?

Geogebra is a free package you can download, and, Screen Capture + Print is a great free screen capture utility.You cay then post the picture using the little green camera:-

Thank you Mr. Randall for your reply.

The reply to Mr.SEMWAL also holds good for your quiery also.

thanks,

DHAYANANDHAN.S

CR4 MEMBER.

Like this then?

YES Mr. RANDALL,

YOU ARE RIGHT.

DHAYANANDHAN.S,

CR4 MEMBER.

Hi Randall,

Thanks for sharing, we all will benefit from this software, I'm very bad at math, but now I will be more lazy.

I already downloaded and tried it; awesome, thanks.

Yahlasit

Mr dhayanandhan with the changed variables it should be like this

{a*Cos^-1(r-x/2)/r}/180 - √(rx-x²/4)*(r-x/2) + {A*Cos^-1(R-x/2)/R}/180 - √(Rx-x²/4)*(R-x/2)

a= area of circle 1

A= area of circle 2

Dear Mr. Rakesh Semwal,

Your sketch is right, indicating the distance x

in the horizontal line. I also made a sketch

in the autocad format similarly but it is not

getting up loaded. If you send your personal

E-Mail, I can send my sketch. Now the

question from me was "what is the area of the shaded

portion of the intersecting circles, as seen in your sketch.

In deed you Mr. Randall have taken much pains.

I thank you for your response.

DHAYANANDHAN.S,

CR4 MEMBER.

This is a similar but I am sure simpler question, and if I were better at math, the answer is already here, I just cannot see it.

If two circles, of equal diameter intersect at each other's center,what is the length of the arc formed beginniing at the point where they first intersect, and ending at the next point of intersection.similar to the previous question, but not the area, simply the length of the curved line is desired to be known.

Thanks

Stu

This has been very helpful, but I can't seem to resolve the equation to find out what it would be if I have the area of the shaded question and want to find X.