Question

Formula to find circumradius of equilateral triangle

Answer 1

The circumradius of a triangle is the radius of the circle circumscribing the triangle. We are given an equilateral triangle of side 8cm



Here ∆ ABC is an equilateral triangle.

O is the centroid of the ∆ABC.

We know that, the centroid of the the triangle is also the circumcentre for an equilateral triangle. Hence, O is the circumcentre .

Let the radius of the circle be r.

We know that in an equilateral triangle, median is also an angle bisector.

Hence, angle OBC= 1/2 angle ABC=30°.

Also , in an equilateral triangle the median is perpendicular to the base. Therefore AD_|_ BC.

∆OBD is right angled triangle.

In ∆OBD, Cos 30=adjacent / hypotenuse = BD/ r ( see figure)

Also, Cos 30 = √3/2 and BD =4

Therefore,

BD/r= 4/r = √3/2

r= 8/√3

Hence , the circumradius is 8/√3 cm.