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Help needed constructing tangents. Geometry or formulae?

Paintman Avatar
Paintman 17 1.5k 180 United Kingdom
3 Jul 2019 9:46PM
I need to find the radius of the red circle either using geometry or a maths formula.

I used to use a CAD program that allowed me to find the radius of a circle when given two circles ( in blue ) and a straight line ( vertical in blue ). The circles are the same distance from the vertical line and the circles are the same size. This would mean the centre of the unknown circle is somewhere along the horizontal blue line. The unknown radius has to touch the intersection of the two straight lines and be tangental to the two circles.

The new CAD program I use doesn't have this tool so I have to try and find the radius by trial and error, which is a slow and inaccurate process.

I have supplied two images, one with one circle and one with two to illustrate the above.

If anyone could point me in the right direction via a Youtube tutorial or some other means I'd be gratefulSmile

I have tried to find the answer via Google, etc., but I can't seem to find an answer to this particular problem. The fact the CAD program I originally used could do this suggests there is either a mathematical or geometric solution.


altitude50 Avatar
altitude50 19 23.9k United Kingdom
4 Jul 2019 8:00AM
From what I remember from school 65+ years ago, to find the centre of the red circle, (my black circle) if that is what is needed, on paper, draw a straight line so it crosses the circle, then using compasses draw two equal part circles using the points where your new straight line crosses, slightly overlapping, then a line at 90 degrees originating from the two new intersections will cross your old straight blue line at the centre of the large circle. (My grey line.). If you do that twice at different points then you are there! Or am I missing something? (diagram not completely accurate.)21670_1562223588.jpg
Tianshi_angie Avatar
4 Jul 2019 10:13AM
Putting in the question 'finding the radius of a circle?' produced a link to this
which has me very confused and it is all such a long time ago! But it may help you.
brian1208 Avatar
brian1208 20 11.8k 12 United Kingdom
5 Jul 2019 12:16PM
try this


Paintman Avatar
Paintman 17 1.5k 180 United Kingdom
7 Jul 2019 10:08AM
Thanks for your answers but they don't address the very specific problem in my post above.

The blue lines are the ones I start with and the problem is to find the circle that is tangental to the two blue circles and the vertical blue line.

It is easy to find a circle that is tangental to the two blue circles only, but adding the vertical blue line and for the circle to be tangental to all three entities means there can only be one radius value for this problem.

If the two blue circles are a different size ( but equal in diameter ) to the above and further away or closer to the vertical line, then the radius of the red circle will also change, but will be specific to each new set of dimensions.


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