Question

An equilateral traingle of side 9cm is inscribed in a circle. Find the radius of the circle.​

Answer 1

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radius of circle = side of equilateral triangle inscribed in that

therefore, radius = 9cm

Answer 2

Answer:

Step-by-step explanation:

Correct option is A)

△ABC is an equilateral triangle.

AB=BC=CA=9cm

O is the circumcentre of △ABC

∴OD is the perpendicular bisector of the side BC.

In △OBD and △OCD

OB=OC(Radius of the circle)

BD=DC(D is the mid point of BC)

OD=OD(common side)

∴△OBD≅△OCD(SSS congruence criterion)

∴∠BOD=∠COD

=>∠BOC=2∠BAC

                      =2×60

                      =120(The angle subtended by an arc at the centre is the double the angle subtended by it at any point on the remaining part on the circle)

∴∠BOD=∠COD

                     =

2

∠BOC

​

                     =

2

120

​

                      =60

BD=DC=

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          

Hence,The radius of the circle is 3

3

​

cm

solution