AIME 1983 Problem 12

Diameter $AB$ of a circle has length a $2$-digit integer (base ten). Reversing the digits gives the length of the perpendicular chord $CD$. The distance from their intersection point $H$ to the center $O$ is a positive rational number. Determine the length of $AB$. [asy] draw(circle((0,0),4)); draw((-4,0)--(4,0)); draw((-2,-2sqrt(3))--(-2,2sqrt(3))); draw((-2.6,0)--(-2.6,0.6)); draw((-2,0.6)--(-2.6,0.6)); dot((0,0)); dot((-2,0)); dot((4,0)); dot((-4,0)); dot((-2,2sqrt(3))); dot((-2,-2sqrt(3))); label("A",(-4,0),W); label("B",(4,0),E); label("C",(-2,2sqrt(3)),NW); label("D",(-2,-2sqrt(3)),SW); label("H",(-2,0),SE); label("O",(0,0),NE);[/asy]