Question

In fig. AABC, LBAC= 30'
show that BC is the radius
of the circumcinci ofa BC
where centre is O.​

Answer 1

Answer:

Here ∠BAC = 30°

And we know that the angle subtended at the centre of a circle by a chord has measure twice that of an angle subtended on the perimeter by the same chord .

Hence

So ∠BOC = 2

∠BAC⇒∠BOC = 2×30°

= 60°

Now in ∆BOC,

Since OB = OC

=radius of the circumcircle

Hence ∠OCB =∠OBC (angles opposite to equal sides are equal)

Now ∠OBC+∠OCB+∠BOC = 180°(sum of interior angles of a triangle)

⇒∠OBC+∠OCB=180°−60°=120°

   ⇒∠OBC=∠OCB =120°2=60°

So ∠OBC = ∠OCB=∠BOC

Thus OB=OC=BCHence BC is the radius of the circumcircle

Step-by-step explanation: