Illustrator doesn't do tangents.

 

No, not really but you can quite easily construct tangents:

Start off by drawing a circle of the required radius.

With Smart guides turned on, use Line or Pen tool to draw radii at the required angles.

Rotate-copy the radii each by 90° about the points where they intersect the circle and bingo.

Now all you have to do is a bit of Pathfinding to get rid of the bits you don’t want.

Combo,

The straight answer to your question is: Ridiculous as it seems, no. Illustrator's so-called Arc Tool is one of the lamest drawing tools I've ever seen in a drawing program. It is what it is, and nothing more. Practically useless.

The Round Corners effect is almost as absurd. On anything other than a 90 degree corner, it does not yield what anyone in his right mind would expect as the numerically specified "radius." Often, it's "rounded corners" are not even round.

JET

CombinatoristAZ wrote:

 

... Imagine two line segments with their ends meeting at a 45 degree angle. I want to to draw an arc inside that angle.

Turn the Smart Guides on, with The Arc tool move the cursor over one of the lines and when the Smart Guides say "path", click on it where you want the arc to start and drag holding Shift until the Smart Guides show a straight line indicating alignment with the intersection point of the lines, then release the mouse button to create the arc.

Take the Scissor tool move it over the intersection between arc and line and when the Smart Guides say "intersection" click there to cut the arc. Then make sure the unneeded part is selected and press Delete until it is gone.

If the arc is not oriented properly, while drawing it press X

another way, CS5 and up

Here's how I would do it in InDesign, you could probably also do this in Illustrator, but I could not get the rotation to anchor in the lower left corner. BTW, I believe there is an InDesign plug-in specifically for math text.

Draw a horizontal line, duplicate it. Draw a square white box the same size as your line on top of the line, group the line and box. Draw a circle and delete two of the anchor points to make an arc, send it to the back. Simply select the box and line group and rotate from the lower left corner to create any angle you want.