Question

2 An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.
Let ABC be an equilateral triangle inscribed in a circle of radius 6 cm I​

Answer 1

Answer:

see below

Explanation:

Let ABC be an equilateral triangle inscribed in a circle of radius 6 cm . Let O be the centre of the circle . Then ,  

OA=OB=OC=6cm

Let OD be perpendicular from O on side BC . Then , D is the mid - point of BC. OB and OC are bisectors of  ∠B and ∠C respectively.

Therefore, ∠OBD=30  

o

 

In triangle OBD, right angled at D, we have ∠OBD=30  

o

 and OB=6cm.

Therefore, cos(OBD)=  

OB

BD

​  

 

⟹cos(30  

o

)=  

6

BD

​  

 

⟹BD=6cos30  

0

 

⟹BD=6×  

2

3

​  

 

​  

=3  

3

​  

cm

⟹BC=2BD=2(3  

3

​  

)=6  

3

​  

cm

Hence, the side of the equilateral triangle is 6  

3

​  

cm