Let O be the centre of thecircumcircle of ΔABC. Remember: In a circle, the angle subtended by the arc at the centre is twice the angle subtended by it at any point on the remaining circle. In ΔABC,∠A=30° ∴ ∠BOC=2∠A=60° In ΔBOC,OB = OC = 10 cm(Circum-radius of the circle) ⇒ ∠OBC = ∠OCB Remember: Equal sides have equal angles opposite to them. ∴ ∠BOC = ∠OBC = ∠OCB = 60° ∴ ΔBOC is an equilateral triangle ⇒ BC = OB = OC = 10 cm Trick : By sine rule:
a
SinA
=
b
SinB
=
c
SinC
=2R where a is the side opposite to angle A and R is the circumradius ∴