Find the radius of a circle given a known smaller circle and other information. There is a large circle with two smaller circles on the inside edge (each $r=6$), the distance between each circle being $50$ (that is directly not along the curvature of the outer circle) and the base of the circles to the 'top' of the outer circle being $15.2.$ I need to find the radius of the outer circle. How would I go about doing that? Cannot use the Intersecting Chord Theorem BTW. This is based off a bearing. The outer circle being the outer raceway, the inner circles being the balls and the the block in the middle being a gauge block. Please ignore the crudity of the diagram. Units unimportant but all the same (being a bearing, there're probably in mm). Thank you in advance. LLAP & DFTBA !Original diagram

Let's call $O$ the center of the circle you seek, $I$ the center of the right small circle, $R$ the radius of the large circle, $H$ the height between base and top of circle, $P$ midpoint between the two small circles and $d=PI$.

You have the triangle $PIO$ which has a right angle at $P$.

$PI=d$, $OI=R-r$ and $PO=R-H+r$

Then you have $(R-r)^2=d^2+(R-H+r)^2$ or $(R-r)^2-(R-H+r)^2=d^2$

That is $(R-r+R-H+r)(R-r-R+H-r)=d^2=(2R-H)(H-2r)$

$R=\dfrac{d^2}{2(H-2r)}+\dfrac H2$