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If a circle is inscribed in a square, then the diagonal of the square contains a diameter of the circle.

Question

If a circle is inscribed in a square, then the diagonal of the square contains a diameter of the circle.

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Solution

Yes, that's correct. If a circle is inscribed in a square, the diameter of the circle is equal to the side of the square. Since the diagonal of a square is the square root of twice the side length, it follows that the diagonal of the square is longer than the diameter of the circle. Therefore, the diagonal of the square contains the diameter of the circle.

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