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Sep 5, 2016 at 5:28 comment added Parcly Taxel Suppose R is equidistant from P and Q, but not at the midpoint. Then the asked-for point exists. But if I move R closer and closer to the midpoint, the asked-for point goes farther and farther away from PQ, until the time when R is on PQ, at which point the circumcentre is infinitely far from PQ and doesn't exist as a real point.
Sep 5, 2016 at 5:21 comment added Mahmudul Hasan I don't understand 2nd and 3rd problem. Can you please explain a bit. In second problem I see this way- if R was midpoint on the line PQ, then I guess there is no point. But, if R is equidistant from both P and Q but not midpoint, then one point is possible in opposite side of R.
Sep 5, 2016 at 5:12 history edited Parcly Taxel CC BY-SA 3.0
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Sep 5, 2016 at 5:03 history answered Parcly Taxel CC BY-SA 3.0