Question

13. An equilateral Triangle of
side 9cm is ipscribed in a circle
then the radius of the circle is​

Answer 1

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/ 2=120/2 =60°

BD = BC =BC /2 =9/ 2cm

in ∆ BOD

sin angle BOD = sin 60° = BD /OB

√3/2 = 9/2\OB

OB = 9/2*2/√3 = 3√3 cm.