Finding the Intersection of Two Circles: A Challenge

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The discussion revolves around finding two points on separate non-intersecting circles such that the distance between them is a specified value 'k'. Participants clarify whether the problem is based on Euclidean geometry or if Cartesian coordinates can be used. They emphasize the importance of showing prior work to better guide the problem-solving process. Key constraints are highlighted, indicating that the distance between the points must fall within a specific range determined by the circles' radii and the distance between their centers. The conversation encourages a collaborative approach to problem-solving.
mamali
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hi everyone !

we have two circles that doesn't have intersections now we want to find a point on each circle that the distance of this two points are 'k' please help me . . .
 
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welcome to pf!

mamali said:
hi everyone !

we have two circles that doesn't have intersections now we want to find a point on each circle that the distance of this two points are 'k' please help me . . .

hi mamali! welcome to pf! :wink:

Is this an old-fashioned Euclidean geometry question, or are we allowed to use Cartesian (x and y) coordinates?

Either way, you have to do some of the work yourself …

show us what you've tried. :smile:​
 
Let the radii of the two circles be r_1 and r_2 and the distance between the centers be R. Then there cannot be a point on one circle and a point on the other so that the distances between the points is less than R- (r_1+ r_2) nor greater than R+ (r_1+ r_2). Do you see why? For distances between those numbers, as tiny-tim says, we would have to see how you would approach this problem yourself so we can know what kinds of hints will help.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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