Question

If the length 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 :

• A. Equal to the side of the cube
• B. √3 times the side of the cube
• C. times the side of the cube
• D. impossible to find from the given information

Answer 1

The correct option is A Equal to the side of the cube

The side length of a cube = AD = a

The diagonal length of a cube = AG = $a\sqrt{3}$

DF = AG = CE = $a\sqrt{3}$

The triangle formed was an equilateral triangle.

The circumradius of an equilateral triangle = $\frac{s\sqrt{3}}{3}$

Therefore, the circumradius of that triangle = $\frac{a\sqrt{3}\sqrt{3}}{3}$
= Side of a cube