I gave Abstract pacman a go today.
I am rusty in trigonometry and I came up with all sorts of solutions to this problem but was too lazy too look up whether I remembered trig laws correctly and came up with the simplest thing i could.
I started with the assumption that the the intersection point of the two circles would be such that the angle to that Point of Intersection would be radians from the origin's of both circles. This was a bit of intuition as to what yields maximum area, the image helped. I also assumed the circle intersected with both axis.
That means if it's in the 4th (lower right/negative y,positive x) quadrant the POI would be (
Let's define the inner circle's radius as .
That means looking at the inner circle you could build a triangle from the origin to (,). since the angle is 45° it is and isosceles with as the hypotenuse and as the two equal sides.
Since we assumed the circle intersected with the y axis we can build the relation that +
we can now solve for as we have
I screwed up by calculating when i should have done and got ~1.17157 or 1.172 rounded up to 3 digits instead of 1.657.
I also forgot to double for diameter which results in 3.314 as the final answer.
My point is let anyone post a solution maybe just flag or differentiate ones that come from people who didn't solve correctly. I haven’t checked whether anyone posted this exact solution yet but realistically this could have happened to someone else with a unique solution who failed to submit a correct answer or took a peek at solutions.