# Circle tangent to line and twin circle

I really need to 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 (blue color)

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

Beside know the diameter of blue circle, I also can know the center angle or XY center coordinates. Please let me know

Thanks on advance

Pedro

## 2 Answers

The center of the pink circle is at the intersection of a vertical at distance $r$ ($35/2$ mm) of the pink line, and a circle of radius $2r$ concentric with the blue circle.

To find this intersection numerically, solve

$$(x-x_c)^2+(y-y_c)^2=4r^2,\\x=x_v+r,$$ which is trivial. • A picture is worth a thousand words ... therfore ... Your solution is better than mine – Donald Splutterwit Feb 21 '17 at 22:53
• @DonaldSplutterwit: mh, I added text as well ;-) – Yves Daoust Feb 21 '17 at 22:54

Draw a line parallel to the pink line that is at a distance of 17.5 from it & on the right hand side. Now set your compass to 35 and place the center at the center of the small blue circle & mark off where it intersects the line; This will give you the center of the pink circle.

To construct the center of the green circle ... set your compass to 80-17.5=62.5 & place the center at the cross & draw this circle. Now do the same as last time ...set your compass to 35 and place the center at the center of the small blue circle & mark off where it intersects the circle (you have just drawn); This will give you the center of the green circle.

I have assumed that the radii of the pink & green circles are 35.