To begin, open Inkscape and select the Pencil tool. You will need to draw either a horizontal or a vertical line. (Due to limitations in the software, this method will NOT work with diagonal lines. However, after you have made your symmetrical arc, you can always rotate it into the correct position later on).
To draw a horizontal line, use the Pencil tool to click a point on the screen, then hold the CTRL key and click on another point to the right of your original location. The CTRL key will help keep the line in a horizontal position (or a vertical position, if you are drawing a vertical line).
Next, we need to switch to the Node tool (F2) to add a central node to the line. With the node tool, click on your line, and then click on the icon at the top of the screen to "Insert new nodes into selected segments":
This will place a new node in the middle of your line:
Make sure the central node is still selected before proceeding to the next step (the node will be blue when selected). Now, click on the icon at the top of the screen to "Make selected nodes symmetric":
This will change the appearance of the node from a diamond to a square. You should also notice a few small circular icons on either side of the node. These are called node handles:
To turn the line into an arc, we are going to select and drag the central node while holding the CTRL key on the keyboard. Make sure that the central node is the only node selected for this part (otherwise you will be moving the entire line):
Now it's time to edit the fullness of the arc. For this step, you will be clicking and dragging a node handle while holding CTRL on the keyboard. Remember that the node handles are the small circular icons on either side of the node.
You only have to choose one node handle to drag. The other node handle will automatically adjust along with it (this is what is meant by a "symmetrical node").
In the example below, I've dragged the right node handle to make the arc more full:
This is what the completed symmetrical arc looks like:
I can see this method being useful for creating bookmark or cross diagrams. If you can find a vertically or horizontally positioned chain within a doily diagram, this method can also be used there. Subsequent chains can be copy/pasted from the first chain and rotated and placed as needed.
Here is an example of a simple edging diagram containing symmetrical chains:
Only the first ring, chain, and picot set were drawn. I then grouped the first set, duplicated it, and moved each repeat into position using the arrow keys.
If you have questions about anything contained in this post, feel free to leave them in the comments section below.