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Answer:
We have ,AB=x units and BC=1unit. So,AC= (x+1)units.
Now ,OD=OC (radii of the same semicircle)
=1/2AC= 1/2 ( x+1)units
And,OB= (OC -BC)=(x+1/2-1) units=1/2(x-1) units
BD² =(OD² -OB²)=1/4(x+1)² -1/4(x-1)²
=1/4{(x+1)² -(x-1)²}=(1/4*4x)=x
BD=√x
Thus,we have proved that BD= √x