# Circle tangent to corner radius and inner circle

I really tried to find documentation for this problem, but can't found a specific solution for this specific issue.

I have a: radius (fillet between 2 lines) with R80mm (blue color) circle tangent to this fillet with diameter 35mm (green color)

What I need: I need to calculate the red circle, that also has diameter 35mm. This circle must be tangent to fillet (blue) and inner circle (green)

Please click on 'Graphic' to check the sketch.

Graphic

Please let me know

Thanks on advance

Pedro

## 3 Answers

Let $R$ be the radius of the fillet and $r$ be the radius of the small circles. The angle $\theta$ between the line through the center of the fillet to the center of the green circle and the common tangent of the two small circles satisfies $$\sin\theta={r\over R-r}.$$ Once you have this angle, you can find the red circle’s center either by reflecting the green circle’s center in this line or by rotating it through an angle of $2\theta$ about the fillet’s center.

According to my guess on your description, I arrive at the following picture:- We can apply cosine law to find $\theta$ from $\triangle OGR$.

Once it is known, the length of the purple line can also be found. That means we know precisely where the center of the red circle is (from OG).

Thanks by both answers! I tried the 1st answer and it's very easy! Amazing! I expected some complicated math, but fortunately not!

Thanks once again Best regards Peter