Draw a triangle and think about how the largest possible circle would fit.
Incenter
Let's draw a triangle formed by the three pathways and then sketch the largest circle that fits inside the triangle.
We can see that the largest possible circle touches all three sides of the triangle, so the distance of the center from all three sides is the radius of this circle.
Since the center of this largest circle is equidistant from the three sides of the triangle, this point is the incenter of the triangle.
According to the Incenter Theorem, we can find this point as the point of concurrency of the three angle bisectors of the triangle.
Maggie can use the incenter of the triangle formed by the pathways to create the largest possible circular flower bed.
