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# A circle problem!!!

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Two circles of radius $$1$$ are centered at $$(4,0)$$ and $$(-4, 0)$$. How many circles are tangent to both of the given circles and also pass through the point $$(0, 5)$$?

Jul 25, 2019

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Two circles of radius $$1$$ are centered at $$(4,0)$$ and $$(-4, 0)$$.
How many circles are tangent to both of the given circles and also pass through the point $$(0, 5)$$?

4 circles are tangent to both of the given circles and also pass through the point $$(0, 5)$$:$$\begin{array}{|l|lcll|} \hline 1 & x^2+\left(y-\dfrac{5}{3}\right)^2=\left(\dfrac{10}{3}\right)^2 \\ \hline 2 & \left(x+1.0328\right)^2+\left(y-1\right)^2\ =\ \left(4.13118\right)^2 \\ \hline 3 & \left(x-1.0328\right)^2+\left(y-1\right)^2=\left(4.13118\right)^2 \\ \hline 4 & x^2+y^2=5^2 \\ \hline \end{array}$$

Jul 26, 2019
edited by heureka  Jul 26, 2019