TITLE: The radius of a circle passing through a circle and the centre point of another smaller circle
QUESTION [0 upvotes]: My idea was determining the equation of the smallest circle of which it might determine the equation of the moddle circle but I was not pretty sure

REPLY [1 votes]: $$AC=2\sqrt{11^2-(11-8)^2}=2\sqrt{112}.$$
$$AB^2=\sqrt{112+4^2}=\sqrt{128}.$$
Thus, $$R=\frac{AB\cdot BC\cdot AC}{4S_{\Delta ABC}}=\frac{128\cdot2\sqrt{112}}{4\cdot\frac{4\cdot2\sqrt{112}}{2}}=16.$$
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