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Locus amid two intersecting circles (Posted on 2021-04-30) Difficulty: 3 of 5
Given a circle and a point K inside it. An arbitrary circle equal to the given one and passing through the point K has a common chord with the given circle. Find the geometric locus of the midpoints of these chords.

No Solution Yet Submitted by Danish Ahmed Khan    
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Hints/Tips Guess without proof | Comment 2 of 5 |
Can't prove it but my guess just from sketching on paper is that these points form a circle, centered on the midpoint between K and the center of the original circle, with a radius half that of the original circle.  

e.g. if you have a circle with radius 10 centered on the origin, and place K at (6,0), you end up with a circle of radius 5 centered at (3,0).  

  Posted by tomarken on 2021-04-30 08:55:38
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