Functions, circles, equations question

The line with equation x = -a is the equation of the side BC of an equilateral triangle ABC circumscribing the circle with equation x^2 + y^2 = a^2.

1. Find the equations of AB and AC.
2. Find the equation of the circle circumscribing ABC.

The line with equation x = -- a is the equation of the side BC of an equilateral triangle ABC circumscribing the circle with equation x^2 + y^2 = a^2.
If AB touches the incircle at M, M is (a cos 60, a sin 60) and A is (2a, 0)
AB passes through M(a/2, asqrt3/2) and A(2a, 0) so its equation is given by
y -- 0 = (x -- 2a)(asqrt3/2 -- 0) / (a/2 -- 2a)
OR AB is y sqrt(3) = x -- 2a ANSWER
AC then is y sqrt(3) = 2a -- x ANSWER

2. Find the equation of the circle circumscribing ABC.
Circumscribing circlr is x^2 + y^2 = (2a)^2 OR x^2 + y^2 = 4a^2
Additional Details
Why does b = 2a? Because in centre of equilateral triangle trisects the median through A.

1. assuming A's coordinate is (b,0) then b = 2a
so AB's equ is y = -sqrt(3)/3 x + 2asqrt(3)/3
AC's eqn is y = sqrt(3)/3 x - 2asqrt(3)/3

2. x^2 + y^2 = 4a^2