Find the relation between a side and the circumradius of an equilatera

1.	Find the relation between a side and the circumradius of an equilateraltriangle.(3)
Answer» Let ABC is an equilateral ∆ whose each side =x units. O be the circumcenter and OA=OB=OC= r. Draw OD perpendicular on BC. Now BD=BC/2=x/2. In right ∆ ODB BD/OB=cos30° or. (x/2)/r=√3/2 or. x/r=√3 or. x=√3.r or. Side of an equilateral ∆ = √3 × Circumradius of that ∆.

Find the relation between a side and the circumradius of an equilateraltriangle.(3)

Answer»

Let ABC is an equilateral ∆ whose each side =x units. O be the circumcenter

and OA=OB=OC= r. Draw OD perpendicular on BC. Now BD=BC/2=x/2.

In right ∆ ODB

BD/OB=cos30°

or. (x/2)/r=√3/2

or. x/r=√3

or. x=√3.r

or. Side of an equilateral ∆ = √3 × Circumradius of that ∆.