For the four circles \(M , N , O\) and \(P ,\) following four equations are given Circle \(M : x ^{2}+ y ^{2}=1\) ; Circle \(N : x ^{2}+ y ^{2}-2 x =0\) ; Circle \(O : x ^{2}+ y ^{2}-2 x -2 y +1=0\) ;Circle \(P: x^{2}+y^{2}-2 y=0\) If the centre of circle \(M\) is joined with centre of the circle \(N\), further centre of circle \(N\) is joined with centre of the circle \(O ,\) centre of circle \(O\) is joined with the centre of circle \(P\) and lastly, centre of circle \(P\) is joined with centre of circle \(M ,\) then these lines form the sides of a

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.