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Beautiful Geometry 1
Four Squares
Four squares. What’s the angle?
SOLUTION
Let the three squares touch at point O. Let ABCD be the fourth square, and A be the common vertex of the three squares. Let c be the circle with center O and radius OA. We have ∠BCA = 45°, and then C \in c. Therefore, ∠ACM = 90°, where AM is the diameter of c. Since ∠ACD = 45°, we get ∠DCM = 45°.
