For the four circles \(\mathrm{M}, \mathrm{N}, \mathrm{O}\) and P , following four equations are given : Circle \(\mathrm{M}: \mathrm{x}^{2}+\mathrm{y}^{2}=1\) Circle \(\mathrm{N}: \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}=0\) Circle \(\mathrm{O}: \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-2 \mathrm{y}+1=0\) Circle \(\mathrm{P}: \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{y}=0\) 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 :

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Circle

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 :

Answer: (A)

Completing squares in each equation gives the centres

M (0, 0)

N (1, 0)

O (1, 1)

and

P (0, 1)

. The joins taken in that order have lengths

M N = N O = O P = P M = 1

and the two diagonals

M O

and

N P

both measure

2

. A quadrilateral with four equal sides and equal diagonals is a square.

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option