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Beautiful Geometry 1

Puzzle Prime April 25, 2023

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Section: School Category: Mini Course

Tags: Featured, Geometry

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 $∠DCM = 45°$ .

Four Squares

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