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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 27, 2019
 #1
avatar+23339 
+1

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)?

 

answer see: https://web2.0calc.com/questions/a-circle-problem#r1

 

laugh

 Jul 28, 2019
 #2
avatar+104937 
+1

Hey heureka.....I understand how you got the equations for the first and last circles in your answer.....could you show how you got the equations for either (2)  or (3)   ????

 

 

cool cool cool

 Jul 28, 2019
 #3
avatar+23339 
+3

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)?

 

A long time ago I wrote a program, see table, the calculation of the (Problem of Apollonius) I have derived by means of the vector calculation.

The third circle has the center (0, 5) and the radius 0.

 

1. Kreis: Mittelpunkt M1 und Radius r1: x1 = 4 y1 = 0 r1 = 1
2. Kreis: Mittelpunkt M2 und Radius r2: x2 = -4 y2 = 0 r2 = 1
3. Kreis: Mittelpunkt M3 und Radius r3: x3 = 0 y3 = 5 r3 = 0

\(\begin{array}{|c|l|c|c|c|} \hline & \text{Index } & x\text{ center} & y\text{ center}&r \text{ radius}\\ \hline 1&+++&0&1.66667&3.33333 \\ \hline 2 &&-8.88178e-16&1.66667&3.33333\\ \hline 3 &++-&0&1.66667&3.33333\\ \hline 4&&-8.88178e-16&1.66667&3.33333\\ \hline 5&+-+&-1.0328&1&4.13118\\ \hline 6&&-1.0328&1&4.13118\\ \hline 7&+--&-1.0328&1&4.13118\\ \hline 8&&-1.0328&1&4.13118\\ \hline 9&-++&1.0328&1&4.13118\\ \hline 10&&1.0328&1&4.13118\\ \hline 11&-+-&1.0328&1&4.13118\\ \hline 12&&1.0328&1&4.13118\\ \hline 13&--+&0&0&5\\ \hline 14&&0&0&5\\ \hline 15&---&0&0&5\\ \hline 16&&0&0&5\\ \hline \end{array}\)

 

laugh

 Jul 29, 2019
edited by heureka  Jul 29, 2019
edited by heureka  Jul 29, 2019

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