Question

Construct 2 congruent chords in a circle

Answer 1

Assume the center of the circle be OO.

Rotate BB by 90 degrees about OO to get B'B'. i.e construct a point B'B' such that  |OB′|=|OB||OB′|=|OB| and OB′⊥OBOB′⊥OB

Then the problem is equivalent to constructing two chords of equal length through AA and B′B′ that are parallel to each other.

In fact, these are the same chord: the one passing through both AA and B′B′. Rotate it by 90 degree about OO to get the chord through BBperpendicular to the chord through AA.