We make a model of a penny farthing bicycle shown above such that the small circle centred at A with radius, r and the large circle centred as B with radius, R both share a tangent with the x axis and y axis and also share a tangent at point C.
Find the value of R/r.
Teacher notes:
Level of difficulty: Accessible for HL students
Syllabus knowledge required: Pythagoras or similar shapes.
This would be a good starter when doing geometry – students could also explore how this can be plotted on Geogebra and think about possible extensions to create an exploration topic.
You can download a pdf of the solution here.