Question

an equilateral triangle is inscribed in a circle . if thr radius if the circle is 5√3 cm. find the side of triangle ​

Answer 1

Answer:

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