CAT Quantitative Ability Questions | CAT Geometry questions
CAT/2004
Question . 75
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 cubeB : √3 times the side of the cubeC : 1/√3 times the side of the cubeD : impossible to find from the given information
View Answer Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Geometry question
(a) Let the side of the cube be 1. Then, diagonal = √3.
Now we have an equilateral triangle with side √3 and its altitude will be 3/2.
Circumradius = 2/3 × altitude = 2/3 × 3/2 = 1.
Thus, the radius of the circle circumscribing that triangle will be equal to the side of the cube.