Here are my thoughts:

I guess you want to end up with an enclosing curve for extruding, and not a "pattern" of curves containing every part of the original circles.

Heres a "manual" operation.

I suggest to use the "cut curve" option. Select everything and cut it (take a look at the option box and select what's appropriate). (!) Use the orthogonical view when cutting and set you option box to "active view".

Delete unwanted parts of the curves.

Next, use the "attatch curves" options. Attatch one curve to another (one by one).

1) If you get wierd results, reverse the curve direction for one of the curves.
2) If the cut curves aren't close enough for connection;
- either do it all over with the convex overshooting the cirlce curves and cut it all again.
- or pick the appropriate vertices and make the convex curve's end vertice connect to the circle-curve for connection.

There could be an easier way to do this, but I prefer the manual way for the time being.


edit:
looks like you want to have the whole part of the three cirlcles too, so just change the option box to "using last curve" and...

pick a circle curve then shift click the convex curve...
... and then cut it
...and delete unwanted parts of the convex curve

(!) you may want to simply make the convex curve by making a whole circle instead of skratch building the convex curve, in that way the cut curve option will work perfect, as the circle-curve-to-be-a-convex-curve is overshooting and crossing your initial "pyramid" circle.