Equation of A line in an Isosceles Triangle

Question

In an isosceles triangle ABC,the coordinates of the point B and C on the base BC are respectively (1,2) and (2,1).If the equation of the line AB is y=2x, then find the equation of the line AC.

I have tried finding slopes of AB and and BC.Then I found the tangent of Angle between them. As base angles in an isosceles triangle are equal,I equated it with the tangent of the angle ACB.Then I found the slope of AC, but I am getting the wrong answer even after trying 6 times.

Any help is appreciated.

Answer 1

WLOG. $A(t,2t)$

Now use $|AB|=|AC|$