Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.
Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
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.
What lengths do you know?
Look for similar triangles.