A square is inscribed in a circle which is inscribed in a square. Find the ratio of the areas of the two squares.
Solution by Zita Anderson, Charlevoix High School
If you rotate the innermost square 45 degrees in either direction and draw in the diagonals, you are able to see eight congruent triangles. All of these are included in the large square, but only half of them are included in the small square. This gives a ratio of 8:4, which reduces to 2:1. Therefore, the outer square’s area is twice as large as the smaller square.
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