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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)?

 Dec 20, 2018

Here's my best attempt.....


I believe that the answer is 1


When two circles are  tangent....a line drawn  through their centers will pass through the point of tangency...so....let the center of the the circle be (x,y)  and the radius = r


The distance for the center of the circle to  (0,5) will just = r

The distance from the center of this circle to the centers of the given circles will be r + 1


We have this system


(x - 4)^2 + y^2 =  (r + 1)^2

(x + 4)^2 + y^2 = (r + 1)^2

x^2 + (y - 5)^2 = r^2


This is a little messy to solve  [ but not impossible]...so I used WolframAlpha to generate the solution


The center of the circle is (x, y) =   (0, 5/3)    and r = 10/3


Here's a graph :




PS....I can show you how to solve the equations if need be...but it's a little lengthy!!!!




cool coolcool

 Dec 20, 2018

Sorry, that isn't correct

Guest Dec 20, 2018

OK.....maybe someone else can shed some light on this....!!!



cool cool cool

CPhill  Dec 20, 2018

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