Three triangles ABC, CBD and ABD (where D is a point on AC) are all
isosceles. Find all the angles. Prove that the ratio of AB to BC is
equal to the golden ratio.
Gold Yet Again
Stage: 5 Challenge Level:
In the equilateral triangle, draw in the altitudes of the triangle
and taking the radius of the circle as $1$ unit, calculate the
In the square it is easiest to take the side of the square as $1$
unit and then calculate the radius of the circle.
In the pentagon it is easiest to take the side of the pentagon as
$1$ unit, and the chord length $XZ$ as $x$ units and then use
properties of similar triangles. Derive a quadratic equation which
you can solve to find $x$.
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