"Regular triangle",Is it mean that "Equilateral triangle"?

Let $ A' $ and $ B' $ be points on sides $ BC $ and $ AC $ such that $ \angle AOB'=\angle BOA'=10^{\circ} $. Since $ \angle AOB=2\angle ACB=40^{\circ} $, it follows that $ \angle A'OB'=60^{\circ} $ and triangle $ A'OB' $ is equilateral. On the other hand, $ \angle OAB'=\angle OBA'=10^{\circ} $,consequently triangles $ OAB' $ and $ OBA' $ are isosceles ones, so $ AB'=OB'=A'B' $ and $ BA'=OA'=A'B' $. Since $ A'B'\parallel AB $, we have $ \angle A'AC=\angle A'AB'=\angle AA'B'=\angle A'AB $ and $ \angle B'BC=\angle B'BA'=\angle BB'A'=\angle B'BA $, so $ AA' $ and $ BB' $ are the angle bisectors and $ A'=A_1 $ and $ B'=B_1 $.