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I've checked the dictionaries and both words have a common meaning:
arc - a shape or structure resembling an arc.
arch - a curved symmetrical structure spanning an opening and typically supporting the weight of a bridge, roof, or wall above it.
Can both these words be interchangeable?
Here is the Oxford Dictionary definition for arc that you referred to:
arc noun
1A part of a curve, especially a part of the circumference of a circle:
the point where a tangential line touches the arc of a circle1.1 A shape or structure resembling an arc:
the huge arc of the sky
Note that, although definition 1.1 refers to a structure, the word arc in the following example (and in all of the other examples quoted) if followed by of. arc is not an actual structure: it serves only to define the shape of the real structure (the sky).
The definition in the Oxford dictionary would be better written as
the shape of a structure resembling an arc.
Here are the definitions from the Cambridge dictionary: as you can see, there is no (STRUCTURE) meaning for arc.
arc
noun [ C ] (CURVE) the shape of part of a circle, or other curved line.arch
noun [ C ] (CURVED STRUCTURE) a structure, consisting of a curved top on two supports, that holds the weight of something above it.
noun [ C ] (SHAPE) something that has the shape of an arch, often used for decoration:
No. An arch (noun) suggests something that is connected to the ground, like the underside of a bridge or a tunnel. An arc (noun) can be free-floating.
I am a native French speaker, and a translator. I'd like to make a short terminology comparison. In English, for architecture, use arch, as in "pointed arch", in all cases. For geometry, use arc, or bow, like in bow-window.
In French, arc's first meaning is "bow" (cf. archer). Arche (Fr) is used to describe a large, primarily bow structure, typically in a bridge or a large space. But Arc (Fr) is just generic or for smaller construction elements. Pointed arch e.g. is said Arc Brisé (and not Arche). And for geometry as well it is Arc.
Exception: On Paris' Champs Élysees, you have the Arc de Triomphe, Rome has the Arc de Titus, which both are rather Arches (Fr) really by their dimensions, but for that kind of monument Arc is the traditionally used terminology. London has the Marble Arch.
And finally rainbow is said Arc-en-ciel (litt. a bow in the sky). How nice is that !
I hope this can somehow help & that no one will be upset this little linguistic invasion of mine.
