Is the intersection of multiple circles that all intersect a specific point always convex?

Question

Assuming I have some circles whose mutual intersection area is > 0, and each of the circles' edges intersect the same point, e.g. as shown in this picture:

Will the mutual intersection set (edge + interior) always convex?

Answer 1

Circles are convex and the intersection of convex sets is again convex, so yes. In fact it doesn't matter if the area is nonzero or if the edges match up nicely, it's always true regardless since circles are convex.