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# Kindly Requesting Help

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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)?

Mar 3, 2020

#2
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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)?

There are 4 circles.
$$\begin{array}{|l|lcll|} \hline 1 & x^2+\left(y-\dfrac{5}{3}\right)^2=\left(\dfrac{10}{3}\right)^2 \\ \hline 2 & \left(x+1.0328\right)^2+\left(y-1\right)^2\ =\ \left(4.13118\right)^2 \\ \hline 3 & \left(x-1.0328\right)^2+\left(y-1\right)^2=\left(4.13118\right)^2 \\ \hline 4 & x^2+y^2=5^2 \\ \hline \end{array}$$  Mar 4, 2020

#1
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There are only 2 such circles.  Try drawing the diagram in the coordinate plane.

Mar 4, 2020
#2
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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)?

There are 4 circles.
$$\begin{array}{|l|lcll|} \hline 1 & x^2+\left(y-\dfrac{5}{3}\right)^2=\left(\dfrac{10}{3}\right)^2 \\ \hline 2 & \left(x+1.0328\right)^2+\left(y-1\right)^2\ =\ \left(4.13118\right)^2 \\ \hline 3 & \left(x-1.0328\right)^2+\left(y-1\right)^2=\left(4.13118\right)^2 \\ \hline 4 & x^2+y^2=5^2 \\ \hline \end{array}$$  heureka Mar 4, 2020
#3
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Nice, heureka  !!!   CPhill  Mar 4, 2020
#4
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Thank you, CPhill ! heureka  Mar 5, 2020