So I tried two quick ways to gain a result, not knowing what the purpose of the end design is to be.
Attachment 126557 and
Attachment 126559
My design file:
Attachment 126560
For both, I created three circles and aligned to match your image.
I did a 500-step extrusion from bit to small blue circles (I changed the larger to red to show the effect).
I then just used snapping point for the second approach to create the red rectangle that I then rotated around its left corner. As its width was the circle radius, it guaranteed a tangent. The other end was by eye but I could have flipped the approach and gained tangents both ways.
I converted the Rectangle to Editable Shapes (green) and moved one corner into the smaller circle and Cloned and flipped (yellow).
Finally, Add Shapes and made Blue.
I deleted some points to smooth out a bit.
I did the above with all aligned with you image but there is a cleaner construction if you lie things on their sides.
Attachment 126562
The "trick is adding the line centre to centre as you can use Ctrl+Snap to get it horizontal, bringing the other shapes along.
Finally, Clone and vertically flip the bar.
I left out the Add Shapes and made Blue.
Surely, none as slick as Tangent Snap but the obverse may be true than it would be equally difficult to perform the above operations in corelDraw. They are two different tools that have their own domain and range of approaches.
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