An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.
Answers
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
hope you understand ....
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
HOPE YOU UNDERSTOOD !!!!!!!!!!!!!!@@@@@@@@@@!!!!!!!!!!!!!!!!!!!!!!!!!!