It is given that AB is a chord of a circle with centre O and AB is produced to C such that BC = OB
We know that ∠BOC and ∠BCO form isosceles triangle
∠BOC = ∠BCO = yo
We know that OA and OB are the radii of same circle
OA = OB
We know that ∠OAB and ∠OBA form isosceles triangle
∠OAB = ∠OBA = 2yo
From the figure we know that
Exterior ∠AOD = ∠OAC + ∠ACO
It can be written as
Exterior ∠AOD = ∠OAB + ∠BCO
So we get
Exterior ∠AOD = 3yo
It is given that
∠AOD = xo
So we get
xo = 3yo
Therefore, it is proved that x = 3y.