This is another tough nut and perhaps the diagram of the 50p piece will help.
A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing the straight line DE with an arc centred at A and radius AE; replacing the straight line EF with an arc centred at B radius BF ...etc..
The 50p piece can roll in the same chute as a disc of radius $r$. Suppose the seven arcs forming the edge of the 50p piece (the arcs AB, BC etc. ) all have radius $R$ (where $R$=AD=AE=BE=BF...) then you need to find $R$ in terms of $r$. These seven arcs subtend angles of $2\pi /7$ at the centre of the disc and $2\pi /14$ at the opposite edge.
Trigonometric identities. Perimeter. Pythagoras' theorem. Rotations. Sine, cosine, tangent. Mathematical reasoning & proof. Regular polygons and circles. Real world. Games. Visualising.