How to make a line intersect with a path at random angles?

How to make a line intersect with the anchor point of a half circle when you want the line to continue beyond the anchor point of the half circle at an angle to randomly?

Now that I saw your picture, I understand the problem. You must make the careful construction work.

Take a look at this:

Start by drawing your circle. Drag the ruler guides (here dotted lines) so that they snap into its Center C.

Drag another landmark of rule to your point of origin O.

With the Pen or line tool Segment a line of O to T A. setting by the eye as precisely as possible with the end of it A directly selected.

A copy of the line OA rotate 90 °. Using smart guides, drag the new line until it crosses the center of the Circle C.

Direct, select the end of your original line and move it to T until the smart guides say "cross".

Now, with the selected OA line use the scale tool. O-click and drag to 45 degrees by holding the Shift key. Your line will extend over its own length.

In order to take account of the OA line across the circle just use the Reflect tool. Select the line, an Option, click the horizontal guide and copy reflect across the horizontal axis through the dialog box.

Tags: Illustrator

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