I want to be able to represent a door as a triangle, but with the smaller side curved as per the image below.
How can I do this with SVG / Raphael? I understand how to make a triangle but I am unsure what to do with the curved section.

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Create a path, like any other Raphael path (see the Raphael documentation for path), and include an elliptical arc (A) in its definition.
Here is a JSFiddle with an example: http://jsfiddle.net/XzPzE/362/