calculate the length of |AB|

[@STEAMerBear]

Very good! I tried for a few minutes but did not build the cyclic quadrilateral.

[@MrSeezero]

I notice that angle A + angle B = 90 degrees from 2A + 2B = 180 degrees since this is a cyclic quadrilateral. Therefore, the angles of the two crossing lines near the center of the circle are all 90 degrees.