Hi I'd like to know how I find out where 2 circles would intersect

I can show the following example:

So far I have:

Left circle:

x = 250 + 200 * cos(a1)

y = 350 + 200 * sin(a1)

where a1 has 2 values where the angles where the circles intersect

and the right circle:

x = 400 + 200 * cos(a2)

y = 250 + 200 * sin(a2)

where a2 has 2 values where the angles where the circles intersect

from that I have:

250 + 200 * cos(a1) = 400 + 200 * cos(a2)

350 + 200 * sin(a1) = 250 + 200 * sin(a2)

Which is where I get stuck.