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

Solution

## The correct option is C Equal to the side of the cubeThe side length of a cube = AD = a The diagonal length of a cube = AG = a√3 DF = AG = CE = a√3 The triangle formed was an equilateral triangle. The circumradius of an equilateral triangle = s√33 Therefore, the circumradius of that triangle = a√3√33                                                                      = Side of a cube

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