Question

abc is a triangle in which angle bac = 30 show that bc is a radius of the circumcircle of triangle abc whose centre is o. find angle bcc and angle bec

Answer 1

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