The diagram shows a rhombus PQRS with an internal point O such that OQ = OR = OS = 1 unit. Penrose used this rhombus, split into two quadrilaterals, a dart and a kite, to make his famous tiling which fills the plane but, unlike a tessellation, does not repeat itself by translation or rotation.

Find all the angles in the diagram, show that POR is a straight line and show that triangles PRS and QRO are similar. Hence prove that the length of the side of the rhombus is equal to the Golden Ratio