Question

An equilateral triangle inscribes 6 circles of radius 10 cm. Find the length of it's sides.​

Answer 1

Answer:

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Answer 2

Step-by-step 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=30o

In triangle OBD, right angled at D, we have ∠OBD=30o and OB=6cm.

Therefore, cos(OBD)=OBBD

⟹cos(30o)=6BD

⟹BD=6cos300

⟹BD=6×23=33cm

⟹BC=2BD=2(33)=63cm

Hence, the side of the equilateral triangle is 63cm



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