If $A+B+C+D=0$ such that $A,B,C,D$ are points on a unit circle, then the points form a rectangle (geometric proof)

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This question is from Needhams "Visual Complex Analysis" and I'm having trouble understanding the proof in a solution I found. I also know that this question has been posted before but I want to understand the geometric proof.

Specifacally, I don't see how in the first line they get that $P,O,Q$ lie in a straight line? Earlier, there was the question which asked us to show that the points that satisfy $|z-a|=|z-b|$, for fixed complex numbers $a,b$, all lie on a straight line. But thinking back to that didn't help me to understand how they got $P,O,Q$ to lie in a straight line provided that $|P|=|Q|$.

Thanks

Proof

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