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computational geometry, 2-digit lengths, rational 2000 Portugal p2

Source:

October 12, 2020
geometrycircle

Problem Statement

In the figure, the chord [CD][CD] is perpendicular to the diameter [AB][AB] and intersects it at HH. Length of ABAB is a two-digit natural number. Changing the order of these two digits gives length of CDCD. Knowing that distance from HH to the center OO is a positive rational number, calculate ABAB. https://cdn.artofproblemsolving.com/attachments/5/f/eb9c61579a38118b4f753bbc19a9a50e0732dc.png
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