I did work it out in the end.

I ended up drawing two isosceles triangles each way from the centre point (I cheated and measured the length of the flat part on the actual component with digital calipers). I knew the length of all three sides and so used cosine law (and yeah, you bet I had to look

*that* up on the internet!

) to work out the vertex angle.

One I'd done that, I used divide to mark the part of the arc between the intersections of the triangles sides and the circle. Then I just selected the new 'arc' entities and just deleted them. Then I just removed the sides of the triangle, leaving the bases there.