Re-asking a question that I made 2 years ago and couldn't get to an answer. Maybe now someone can reach it!
Two circles, C and Cr intersect each other. C's radius is 1, while Cr's radius is "r". Their tangent lines form an internal angle of 120° at each intersection point. 1) Calculate the distance "d", which is the distance between the centers of both circles, in terms of r. 2) Find where d has a maximum or a minimum. 3) Find the area of the intersection in terms of π

Question

Re-asking a question that I made 2 years ago and couldn't get to an answer. Maybe now someone can reach it!
Two circles, C and Cr intersect each other. C's radius is 1, while Cr's radius is "r". Their tangent lines form an  internal angle of 120° at each intersection point. 1) Calculate the distance "d", which is the distance between the centers of both circles, in terms of r. 2) Find where d has a maximum or a minimum. 3) Find the area of the intersection in terms of π

chillout · Answer

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chillout · Answer

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chillout · Answer

I'm starting to think that this is unsolvable.

chillout · Answer

All right, so I found this: http://www.had2know.com/academics/intersection-angle-two-circles.html Is this of any help?

chillout · Answer

I swear if I get an answer to this I'll become a math teacher.

ganeshie8 · Answer

Cutting out 30 degrees from either ends of the tangent lines, it is easy to see that the angle made by radii segments at the intersection point is 60 degrees :

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