How to add a node where two handles meet

Question

I have two nodes that create a curved edge. I want to add a new node where the handles for these nodes would intersect if they were extended, and then delete the original two nodes. This would turn the curve into a sharp edge.

I can add a new node, eyeball it into place, and delete the two original nodes, but is slow, and seems inexact. Is there a better way?

Answer 1

It is not possible to use Live Corners after selecting one of the points?

Here the explanation from Adobe.com

If not,

• Duplicating the figure a couple of times, following each line as a displacement guide
• After selecting both duplicates, with the Shape Builder Tool and pressing Alt delete the surplus
• Unite this shape with the original one from Pathfinder

Answer 2

See image 1. Circles A,B,C and D contain the anchor points of the blue shape. Let's assume you want to continue straight line segments AB and DC to form a sharp corner.

2. Draw lines AB and DC. To do it exactly have smart guides and snap to points ON, no other snaps!

3. Holding Shift at the same time drag the new line objects with the normal selection tool to bigger sizes to make a crossing

4. With the anchor removal tool remove anchor B and with the anchor type conversion tool make C a corner point

5. Drag C to the crossing of the lines with the direct selection tool

NOTE: This receipe is useless, if you literally want to find the point where the extensions of the handles meet, like in this:

Blue shape can be curved in both sides of B and C, but have tangents, at least one sided tangents. Finding those tangents need something smarter - for example a third party plugin. Check, if Astute Graphics has a good one. I haven't one.

Alternatively you can goto Inkscape. There's a path visualization extension "Draw handles" which really inserts to the image all handles as lines. It's no problem to extend them:

Then you can draw the exact needed add-on shape and make an union: