Question:
If the lengths of diagonals DF, AG, and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be
If the lengths of diagonals DF, AG, and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be
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In problems involving cubes and their diagonals, use the Pythagorean theorem to find relations between the side and the diagonal lengths.
Updated On: Aug 1, 2025
- equal to the side of the cube
- \( \sqrt{3} \) times the side of the cube
- \( \frac{1}{\sqrt{3}} \) times the side of the cube
- impossible to find from the given information
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The Correct Option is B
Solution and Explanation
The lengths of diagonals \(DF\), \(AG\), and \(CE\) are related to the sides of the cube.
The radius of the circle that circumscribes the triangle formed by these three diagonals is proportional to the side of the cube by the factor \( \sqrt{3} \).
\[
\boxed{\sqrt{3} \text{ times the side of the cube}}
\]
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