Question

Match circles M, N, O, P and determine the shape formed by joining their centers in order.

• A. Rectangle
• B. Rhombus
• C. Square
• D. Parallelogram

Hint:

Plotting the centers on a Cartesian plane quickly reveals the geometry for integer coordinates.

Answer 1

The Correct Option is C

Step 1: Find centers: Circle M: $x^2+y^2=1 \rightarrow C_M(0, 0)$. Circle N: $x^2+y^2-2x=0 \rightarrow C_N(1, 0)$. Circle O: $x^2+y^2-2x-2y+1=0 \rightarrow C_O(1, 1)$. Circle P: $x^2+y^2-2y=0 \rightarrow C_P(0, 1)$.
Step 2: Analyze the points $(0,0), (1,0), (1,1), (0,1)$.
Step 3: The sides are $MN=1, NO=1, OP=1, PM=1$ (all equal to 1).
Step 4: The diagonals are $MO = \sqrt{1^2+1^2} = \sqrt{2}$ and $NP = \sqrt{1^2+1^2} = \sqrt{2}$.
Step 5: Since all sides are equal and diagonals are equal, it is a square.