# 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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## 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

Click here👆to get an answer to your 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

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

**A**

## equal to the side of cube

**B**

3

times the side of the cube

**C**

3 1

times the side of the cube

**D**

## impossible to find from the given information

Medium

## 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 :

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 :

Home

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 :

Question

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

Open in App Solution

The correct option is **C** Equal to the side of the cube

The 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 √ 3 3

Therefore, the circumradius of that triangle =

a √ 3 √ 3 3 = Side of a cube Suggest Corrections 0 SIMILAR QUESTIONS

**Q.**In the given figure △ABC is an isosceles triangle with perimeter 44 cm. The base BC is of the length 12 cm.

Sides AB and AC are congruent. A circle touches the three sides as shown. Find the length of a tangent segment from A to the circle.

**Q.**In the adjoining figure, a triangle is drawn to circumscribe a circle of radius

2 c m

such that the segments

B D and D C into which B C

is divided by the point of contact

D are the length 4 c m and 3 c m

respectively. if area of

△ A B C is 21 c m 2

, find the lengths of sides

A B and A C .

**Q.**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

**Q.**Consider the cube given below:

N R , M S and P T

are the diagonals of the cube whose volume is

1728 c m 3

. If a triangle is constructed whose three sides are same as the measure of the sides

N R , M S and P T

, then what will be the radius of the circle circumscribing that triangle?

**Q.**Three cubes with sides in the ratio

3 : 4 : 5

are melted to form a single cube whose diagonal is

12 √ 3 c m

. The sides of the cubes are

## [Solved] 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? https://cracku.in/media/uploads/2015/07/08/geom12.PNG here is my doubt so if a side of equilateral traingle is √ 3* x. its circumradius should be equal to the side of a equilateral traingle?

Question Shubham Nagoria

6 years, 1 month ago

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? https://cracku.in/media/uploads/2015/07/08/geom12.PNGhere is my doubt

so if a side of equilateral traingle is √ 3* x. its circumradius should be equal to the side of a equilateral traingle?

(0) Follow (0) Comment Share Answer Shubham Nagoria 6 years ago Thanks got it 0 Answer Jay 6 years ago

Dear Shubham, Circumradius=a*b*c/4A for a triangle, where a,b,c are sides and A is its area. Hence the answer to the above question is "x". The side of the triangle as you found out is √ 3* x. Hope this helps. :)

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Guys, does anyone know the answer?