Given:
Side of equilateral triangle
=x unit
The radius of the circle (OA or OB or OC)
=y unit
Concept Used:
For an equilateral triangle
All the centers i.e circumcentre, orthocentre, centroid, incentre lie on the same point
Centroid divides median in the ratio of
2:1. Calculation:
According to the question
ABC is an equilateral triangle
So, The center of the circle is also the centroid of
△ABC Since The Height or median of the equilateral triangle
(AD)=√3X∕2 And we know that centroid divides the median into
2:1 ratio
i.e
OA:OD=2:1 ⇒OA:AD=2:3 ⇒y:√3x∕2=2:3 ⇒2y∕√3x=2∕3 ⇒3y=√3x ⇒√3y=x ∴ The correct relation between
x and
y is
√3y=x .