An equilateral triangle of side 9 cm is inscribed a circle. The radius of the circle is (a) 3 cm (b) 3v2 cm (c) 3v3 cm (d) 6 cm
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Answers & Comments
Step-by-step explanation:
△ABC is an equilateral triangle
AB=BC=CA=9cm
O is the circumcentre of △ABC
∴OD id the perpendicular of the side BC
In △OBD and △ODC
OB=OC (Radius of the circle)
BD=DC (D is the mid point of BC)
OD=OD (common)
∴△OBD=△ODC
⇒∠BOD=∠COD
∠BOC=2∠BAC=2×60
∘
=120
∘
(The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle)
∴∠BOD=∠COD=
2
∠BOC
=
2
120
∘
=60
∘
BD=BC=
2
BC
=
2
9
cm
In △BOD
⇒sin∠BOD=sin60
∘
=
OB
BD
∴
2
3
=
OB
2
9
⇒OB=
2
9
×
3
2
=3
3
cm
Verified answer
Answer:
Annyo~ gm khushi (~￣³￣)~
Step-by-step explanation:
An equilateral triangle of side 9cm is inscribed in a circle. Find the radius of the circle. Therefore, the radius of the circle is 3√3 cm.