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The large Circle is Radius 4.51 and the 3 smaller ones 2.06. While not super perfectly to scale….it is very close. On to my question:

Where can I find equations to prove/disprove that 3 or more circles with radius R1 will fit within the bigger circle radius r2?

All 3 are perfect circles and are the same size. while i do not Understand Descartes’ Theorem (never learned that in HS) i was thinking it my be what i am after. Excerpt for the net:if four mutually tangent circles have curvature a, b, c, and d, then…

(a + b + c + d )2 = 2(a2 + b2 + c2 + d 2 ).

My line of thinking is i have 3 mirrors and wish to place them all in a perfectly circular hoop and then fill in with stained glass.

What must the 3 little radius be to fit in the 4th? they do not have to touch the hoop and can be much smaller.

Thanks in advance for your time, and double thanks to any that can help. some links on what i found but was not making headway with: