Question 1096936
<br>From the given information, the center of the circle is O(0,0). Since side BC of the circumscribed equilateral triangle is on the line x=-1, the point of tangency of the circle with side BC is P(-1,0).<br>
Let B be the vertex of the triangle with a positive y coordinate and C be the vertex with a negative y coordinate.<br>
Triangles BPO and CPO are 30-60-90 right triangles, so BP = CP = a*sqrt(3) and OA = OB = OC = 2a.  So B is (-1,a*sqrt(3)) and C is (-1,-a*sqrt(3)).<br>
And since the medians of a triangle divide each other in the ratio 1:2, we know A is (2,0).<br>
Since we now have the coordinates of all three vertices of the triangle, and since we know OB is the radius of the circle circumscribed about triangle ABC, we can answer all parts of the problem.