Question

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
@Jinie_ Nado Saranghae (*･ω･ﾉﾉﾞ☆ﾟﾟ​

Answer 1

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

Answer 2

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.