Question

What is the circum radius of an equilateral triangle whose side is 9cm ?

Answer 1

Answer:

Circum radius of an equilateral triangle whose side is 9cm = 9/√3

Step-by-step explanation:

It is given that side of equilateral triangle is 9cm

From the figure attached with this answer, we can see that, CD is the perpendicular bisector  of <C.

O is the center of circum circle.

OA is the radius

To find the Circum radius

Consider the triangle OAD

<OAD = 30    ( since OA = OC)

<ADO = 90 and <AOD = 60

The angles are 30 , 60 , 90

Therefore three sides are in the ratio,

OD : AD : OA = 1 : √3 : 2

Here AD = 9/2

OD : AD : OA  = 9/2√3 : 9/2 : 9/√3

Therefore the Circum radius OA =  9/√3