A square with side-length 10 cm long is drawn on a piece of paper. How many points on the paper are exactly 10 cm away from two of the vertices of this square?
A. 4 B. 6 C. 8 D. 10 E. 12
E
For each of the four pairs of adjacent vertices, there is one point outside the square and one point inside the square that is exactly 10 cm from each vertex in the pair. Also each of the four vertices themselves is exactly 10 cm from the two adjacent vertices. Hence, there are 12 points in total that are exactly 10 cm from two of the vertices of the square and these points are all distinct. The diagram below shows the positions of these 12 points.
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