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Golden Triangle
Age 16 to 18
Challenge Level 
The three triangles $ABC$, $CBD$ and $ABD$ are all isosceles. Find the angles in the triangles.
The sides $AB$ and $BC$ have lengths $p$ and $q$ respectively. Prove that the ratio $p/q$ is equal to the golden ratio $\frac{1}{2} (\sqrt{5}\ +1) $.
and find the ratio $q/p$.The area of triangle $ABC$ is 2 square units. Find the areas of $CBD$ and $ABD$ exactly (i.e. find the areas in the form \[ a + b \sqrt{5} \]
where $a$ and $b$ are rational numbers)You may also like
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Pythagorean Golden Means
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.
