an equilateral triangle is inscribed in a circle of radius 10m find the length of the side of the equilateral - Maths - Circles

Question

an equilateral triangle is inscribed in a circle of radius 10m
find the length of the side of the equilateral triangle

S. Usha Rani · Accepted Answer

Let the sides of the equilateral triangle be x

i e AB=BC=Ac=xNow, in ∆ABC,∵O is centroid of
∆ABC, ∴AO=23AD (As centroid divides the median in the
ratio of
2:1)⇒AD=32AO=32×10=15mar(∆ABC)=12×BC×AD=12×(x)×(15)=15x2
m2Also, ar(∆ABC)=34x2 m2So, 34x2=15x2⇒x=303=3033=103
mHence, sides of equilateral ∆ is 103 m

an equilateral triangle is inscribed in a circle of radius 10m find the length of the side of the equilateral triangle