A circle in the middle

Geometry Level 3

Three unit circles are centered at (0,1), (3,0) and (3,4).

What is the radius of the circle that is externally tangent to all three of them?

Please provide your answer to 3 decimal places?


The answer is 1.236.

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Mar 7, 2017

By bisecting all the line segments between the centers, and taking the intersection of these bisectors, you find that the point ( 2 , 2 ) (2,2) is equidistant from all the centers. So it will be the center of a circle that passes through all three centers. Its distance to the centers is 5 \sqrt5 , so its distance to the circles (to be externally tangent to them) will be given by:

R = 5 − 1 = 1.236 R = \sqrt5 -1 = \boxed{1.236}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

The point ( 2 , 2 ) (2,2) is equidistant from all the centers, ...

How did you find this coordinate?

Pi Han Goh - 4 years, 3 months ago

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By bisecting all the line segments between the centers, and taking the intersection of these bisectors, you find that the point ( 2 , 2 ) (2,2) is equidistant from all the centers. (I've added this to the solution... Thanks!)

Geoff Pilling - 4 years, 3 months ago

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