Here, `BD = s-b`
`CD = s-c`
`BD*CD = (s-b)(s-c)`
`=>2 = (s-b)(s-c)`
`=>2s(s-a) = s(s-a)(s-b)(s-c)`
`=>2s(s-a) = Delta^2`
`=>Delta^2/s^2 = (2(s-a))/s`
`=>r^2 = 2-(2a)/s`
As, `r` is constant, so `a/s` will be constant.
Let `H_a` is the distance of `A` from `BC`.
Then, `Delta = 1/2*a*H_a`
`=>Delta/s = 1/(2s)aH_a`
It is given that circle is of unit radius,
` :. 1 = a/(2s)H_a`
`=>H_a = (2s)/a`
It means `H_a` will be constant as `a/s` is a constant.
So, locus of vertex `A` will be a straight line parallel to `BC`.
So, option `(a)` is the correct option.