SOLUTION: Circle C has radius √2 Squares with sides of length 1 are to be drawn so that, for each square, one vertex is on circle C and the rest of the square is inside circle C. What
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Question 337647: Circle C has radius √2 Squares with sides of length 1 are to be drawn so that, for each square, one vertex is on circle C and the rest of the square is inside circle C. What is the greatest number of such squares that can be drawn if the squares do not have overlapping areas?
(A) None (B) One (C) Two (D) Three (E) Four
Join the points where the diameters touch the circle.
You will now have a large square of sides 2 (Pythagoras √2, √2, 2 : root 2 squared plus root 2 squared equals 2 squared)
Divide this square into four (half one way and half the other way)
You will now have four equal squares of sides 1 within the circle with each square touching the circle in only one place and no overlap with any of the other squares.
If you follow this and sketch the diagram you should see the answer is four.
