A circle of radius 7 is drawn inside a square so that it just touches all four sides, as shown. What is the side length of the square?
A28
B7
C21
D49
E14
Explanation
Archimedes of Syracusec. 287–212 BCE · Master of Circles“Give me a diameter and I will give you the square that holds the circle.”
The circle and its square are bound together by one fact: since the circle touches all four sides, it stretches the full width of the square, from one side straight across to the other. That full width is the circle’s diameter. The diameter is twice the radius: 2 · 7 = 14. Because that diameter spans exactly from side to side, the side of the square must also be 14. Guard against the trap: the radius (7) reaches only halfway across; the side matches the diameter, not the radius. Takeaway: for a circle inscribed in a square, side = diameter = 2 × radius — a bridge between the round and the straight.
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