Intersecting of 2 cirlces of equal diameter

Homework?

If r is the radius, then the length of the arc is 4(pi)(r)/sqrt(3).

Half of one circle's perimeter I'd say.

The question doesn't make sense. What intersects with what?

do you mean that each circle's circumference passes through the center of the other?

Now that the centers are significant, do they count for the length of arc?

If circles radius is = R

then arc length you ask for is = (2/3)*pi*R

If this is a homework problem, I sincerely hope your teacher makes you present a graphical proof and an explanation of HOW you arrived at the answer.

Intersecting circles

Givens:

1. The circles are of the same diameter.
2. The edge of each circle intersects with the center of the other.

If you draw the proposed problem, you will see that the distance between the centers of the circles is the radius, R, of the circle. Further, the midpoint between the circle centers is R/2. As you can see, this sets up a trigonometric identity problem for which an answer is quite easy to procure.

x² + 0.5R² = R²

x² = R² - 0.5R²

x = Sqrt(R² - 0.5R²)

But the distance between the intersection point of the circles is 2x.

Therefore, the calculation for the distance (D) between the intersection points is:

D = 2*Sqrt(R2 - 0.5R2)

As has been said, you must endeavor to solve these problems with the information you have been given in class. Nothing teaches better than the solution arrived at through blood, sweat and tears.

The fact that you posted your problem here, in it's original form, makes me believe that you are not really trying to learn, but just want to get through school. If this is the case, you'd better give up now. You will be overrun by those who truly want to understand math and science. If you do make it, I think you would find your place in management.

Mike

d= R/2

S = lenght of arc = 2*R Cos¯¹ d/R = 2R Cos ‾¹ 1/2 (in radians)

I was too lazy to draw so I will aplaude(GA) your drafting abilities (becase, I am sure that I answered, first, the question).

It was a good answer, indeed.

Thanks for all your help.This is not homework.I was just curious.I have grandkids in high school.

stu

Oh - I thought is was homework so I was lying.