CBSE Class 9 Answered

ABC is an equilateral triangle.

AB = BC = CA = 9 cm

O is the circumcentre of ABC.

 OD is the perpendicular bisector of the side BC.

(O is the point of intersection of the perpendicular bisectors of the sides of the triangle)

In OBD and OCD,

OB = OC (Radius of the circle)

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

OD = OD (Common)

 OBD  OCD (SSS congruence criterion)

BOD = COD (CPCT)

BOC = 2 BAC

          = 2 × 60°

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

In BOD,

Sin BOD

Thus, the radius of the circle is .