Consider a circle, where the length of diameter PQ is a 2-digit integer. Reversing the digits of PQ one obtains the length of a perpendicular chord RS.

PQ intersects RS at the point T. The center of the circle is denoted by O and it is known that the length of TO is a positive rational number.

Determine the length PQ.

(In reply to computer solution (spoiler) by Charlie)

Ty, Charlie. I confirm having hyperlinked your methodology in the official solution.

Posted by K Sengupta on 2023-01-09 01:43:28