<Qua-2025-776>, hint

Since OCTD is a parallelogram TD=OC, TC=OD, AC//=2DT.

Since AC//DT, <DTA=<OAT=<DAT,  DA=DT, AC=2DT. <ACTD is an isosceles trapezoid, and concyclic. Let T' be symmetric to T about O.

AT'BC and ADTC are congruent, ADTCBT' is a regular hexagon and 

 triangle ABT is equilteral.