Question

In a circle an equilateral triangle of side 9 cm is made. All the points r on the circumference, find the radius.

Answer 1

See the diagram.

Let the side of triangle = a = 9cm

radius = r cm

a = 2 × r cos 30

=> 9 = 2 × r × √3/2

=> 9 = √3r

=> r = 9/√3 = 3√3 cm

Radius of circle is 3√3 cm.

Answer 2

ANSWER

△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= ∠BOC=120°=60°

2 2

BD=BC=BC = 9

2 2

⇒sin∠BOD=sin60°= BD

OB

∴ 3=9

2 2

⇒OB= 9×2

2×3

=3

ans....3 cm