perplexus.info :: Just Math : Integral chords

Integral chords (Posted on 2024-12-06)

A circle with center O has integer diameter. A point P is selected inside the circle such that OP = 12 and there are 5 chords of integer length passing through P with respect to the given circle. Then find the possible radii of all such circles.

No Solution Yet Submitted by Danish Ahmed Khan

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re(3): Solution

Comment 4 of 4 |

(In reply to re(2): Solution by Larry)

Thanks for that. I was misinterpreting the problem.

When I saw chords and point P, I started looking for the partitions being integers (or half-integers). For example D=32, r=16 gives P power 112 with the five integer chords partitioned as (7+16), (8+14), (14+8), (16+7), (4+28).

But of course there are others such as 12+/-4sqrt(2).

Posted by Jer on 2024-12-06 12:48:28

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