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From the image, I need to find radius r.

I have a circle(R) whose center is $(0,0)$ and has a radius $R$.

I need to find radius $r$ of circle(r) which is internal and tangent to the circle $R$.

Circle(r) is also tangent to a vertical line at a distance $a$ from the origin Circle(r)'s centre is on a horizontal line that is distance $b$ from the vertical

I'm not able to find the answer.

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enter image description here

We have $(R-r)^2 = (a-r)^2 +b^2$ and hence $$r = \frac{R^2-a^2-b^2}{2(R-a)}$$

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    thanks for the answer. superb. which software do you use for the drawing ? – 2017-02-28
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    Geogebra. This is open source, free Geometry software. You can download from geogebra.org – 2017-02-28