[creating circles that intersect precisely with other objects]

I'm new to Affinity Designer (and not a graphic artist) but I'm using it to create a template of intersecting lines and circles. I can easily use snapping to intersect lines and squares precisely but I'm having a problem with circles. Snapping works as long as I'm intersecting the circle at the horizontal or vertical edges, however I need to intersect circles at one precise point not in the horizontal/vertical. I've tried adjusting the snapping parameters but it hasn't worked. I've also tried to mathematically calculate the radius but I need more complicated functions with square root, etc, to be exact.

The file I uploaded is the simplest example I have. I want the circle in the upper left to have a center at the upper left corner of the square. I want the radius to be such that it intersects the larger arc at one place (after which I can turn the small circle into an arc...). I can get close but I need it to be exact. Is this possible with snapping?

Thanks!

4 Fold Template AD.afdesign