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Golden Thoughts
Age 14 to 16
Challenge Level 
Consider the following diagram:
Given that the areas of $A1$, $A2$ and $A3$ in the above diagram are equal, show that $${RX\over XS} = {RY\over YQ} = {{\sqrt{5}+ 1}\over 2}$$ so that the points $X$ and $Y$ divide the sides of the rectangle in the golden ratio.
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The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
