TITLE: Does a semicircle have 2 right angles?
QUESTION [9 upvotes]: If you have a line passing through the middle of a circle, does it create a right angle at the intersection of the line and curve?
More generally, is it valid to define an angle created between a line and a curve? Is the tangent to the curve at the point of intersection a valid interpretation (I.e a semi circle has 2 right angles)
I saw it in a debate thread and it got me curious now.

REPLY [7 votes]: As you identify in your question, the real point of contention is the definition of angle. As the other answers have indicated, if your definition includes angles at the intersection of two curves then a semicircle certainly has two right angles.
However, as the controversy on Twitter (a few days ago at time of posting, started because this question was in someone's daughter's primary school homework) indicates, angle as commonly used is often restricted to the intersections of (straight) lines. Under this definition there is no angle at the vertices of a semicircle.
Which definition is more common is an empirical question (and the consensus seems to be that the wider definition is common among professional mathematicians, while the stricter definition might be something a layperson would describe), but to my mind the fact that there exist differing definitions makes your question ill-formed. I think the educational value is to expose the fact that we should be careful with how we think about our definition.