The chord of the contact of tangents drawn from point on the circle $$x^2 + y^2 = a^2$$ to the circle $$x^2 + y^2 = b^2$$ touches the circle $$x^2 + y^2 = c^2$$ such that $$b^p = a^m c^n$$ where $$m, n, p \in N$$, and m, n, p are prime to each other, then the value of 2m + n + 2p - 3 is:

The chord of the contact of tangents drawn from point on the circle $$x^2 + y^2 = a^2$$ to the circle $$x^2 + y^2 = b^2$$ touches the circle $$x^2 + y^2 = c^2$$ then  $$a$$, $$b$$, $$c$$ are in G.P

$$=$$>   $$b^2=ac$$ ....................(1)

Given,  $$b^p = a^m c^n$$ ...........(2)

Comparing equation (1) and equation (2)

p = 2, m = 1, n = 1

$$\therefore\ $$2m + n + 2p - 3 = 2(1) + 1 + 2(2) - 3 = 2 + 1 + 4 -3 = 4

Hence, the correct answer is Option B