Question

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

Answer 1

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°

In ∆OBD,

right angled at D,

we have ∠OBD=30°,and OB=6cm.

Therefore, cos(OBD = BD/OB

⟹cos(30°) = BD/6

⟹BD = 6cos30°

⟹BD = 6 × √3/2

= 3√3 cm

⟹BC = 2BD = 2(3√3) =6√3cm

Hence, the side of the equilateral triangle iis 6√3cm.

Answer 2

the above photo will definately help

........... @chandrani poddar.......ল