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 circl

Step-by-step solution

M   :   x 2 + y 2 = 1   center= 0 ,   0 N   :   x 2 + y 2 - 2 x = 0 ,   center = 1 ,   0 O   :   x 2 + y 2 - 2 x - 2 y + 1 = 0 ,   center = 1 ,   1 P   :   x 2 + y 2 - 2 y = 0 ,   center = 0 ,   1 M N = 1 - 0 2 + 0 - 0 2 = 1 N O = 1 - 1 2 + 0 - 1 2 = 1 O P = 1 - 0 2 + 1 - 1 2 = 1 P M = 0 - 1 2 + 1 - 1 2 = 1 Then, all the sides are equal of a quadrilateral then M N O P is a square.