#### Question

# An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.?

An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.?

#### Answers

Let side = x

x 2 = 6 2 + 6 2 - 2 (6)(6) cos 120 °

x 2 = 72 - 72 cos 60 °

x 2 = 72 - 36

x 2 = 36

x = 6 cm

#1

x/12 = 2/√3

x = 24/√3 = 8√(3)/3

#2

angle between two sides=pai/6

radius=6cm

so side=2 times of 6cos pai/6

(using just cos in triangle)

side=6*root of 3=10.392 cm.

#3

two end points of sides make an angle 120 at the center. suppose o is center.draw a perpedicular line to any side OM is perp.and A be the end point .angle A will be 30 degree. cos30=AM/OA .cos30*OA =AM sqrt3/6=AM so AB=2AM=2*sqrt3/6=sqrt3/3 =1/sqrt3

#4