Or, especially if you have a version without Shape Builder, one (other) way is to (Smart Guides are your friends):
1) Create the circle,
2) Create the line,
3) With the lien still selected, with Scissors Tool cut the line where Smart Guides say intersect, and delete the superfluous part,
4) Repeat 3) for the circle,
5) With the Direct Selection Tool select each of the two sets of coinciding end points and Ctrl/Cmd+J to join.
Jacob's steps are great. Here are some visuals to go along with his instructions.
1) Create the circle. I also made a guide to make everything easier for me.
2) Create the line.
3) Select the circle and use the Scissors tool to cut the circle at the two intersection points.
4) Delete the unwanted segment.
5) Do the same for the unwanted portion of the line.
6) Direct Select each of the two pairs of end points and Join them with Ctrl/Cmd+J.
Draw the line and circle with Strokes only. Select both; go to Object > Path > Outline Stroke. Select all, go to the Pathfinder and select Divide. With the Direct Select tool, select and delete the sections you don't need. Then select all, go to Pathfinder and select Unite. You're left with one shape.
rcraighead has the easiest and probably the most efficient way however it is not complete in that once you ave eliminate the cord and the line segment to make the opening they will be three separate paths two straight lines on either side of the circular arc.
You then have to select it all and then use command or control J to join the three paths as one then you will have what you wish.
The shape builder is very cool in case you do not have version that has this tool.
Before you sue the join command
After you use the join command
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