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: Solution

| Comment 2 of 4 |

(In reply to Solution by Larry)

I don't understand these solutions.

In your last example D=74. r=37.

P is 25 from one end of the diameter and 49 from the other. The power of this point is thus 1225.

Any other chord will have the same power so we seek x*y=1225 when (x+y)<74 and (x+y) is an integer.

I can only find 35*35 which gives only two chords. Am I missing something?

Posted by Jer on 2024-12-06 11:39:41

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