perplexus.info :: Just Math : Circle's convergence

Circle's convergence (Posted on 2023-07-31)

Some parabolas of the form y=x²+bx+c have three distinct intercepts (two x and one y). If for all such parabolas a circle is drawn through these three points, they will have a point in common.

Prove this assertion and find the point.

No Solution Yet Submitted by Jer

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re(2): Solution

Comment 3 of 3 |

(In reply to re: Solution by Jer)

Thanks, but now taking another look I think I have made an error about the claim that the vertex is always in the circle.

I'll have to take another crack at it sometime.

Posted by Brian Smith on 2023-08-02 13:48:58

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