Circle intersections

37ten

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Oct 18, 2017
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If I have three circles, two where all required information is known i.e. co-ordinates, radius, etc. and the third where the only known information is the radius. How do I find the intersections and co-ordinates of the third circle?

A little more information, the two circles are larger than the third and encase the third. The circle should only touch in two places.

I real world terms, I am trying to find the center position of a ball running in a bearing with offset tracks. When the ball is in contact with both tracks.
 

Subhotosh Khan

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If I have three circles, two where all required information is known i.e. co-ordinates, radius, etc. and the third where the only known information is the radius. How do I find the intersections and co-ordinates of the third circle?

A little more information, the two circles are larger than the third and encase the third. The circle should only touch in two places.

I real world terms, I am trying to find the center position of a ball running in a bearing with offset tracks. When the ball is in contact with both tracks.
By that I assume you mean co-ordinates of the center. Have you drawn few sketches to investigate the problem?

In particular draw a sketch where the origin is at the co-center of the larger circles and x-axis is tangent to the little circle. What can you say about the co-ordinate of the center of the little circle?

I do not quite understand the term "intersections of the third circle". Explain more.
 
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