Problem of the Week 1194

A Classic Linkage

Consider a unit circle centered at the origin and a linkage with one point, O, fixed at (-1, 0) and with point B restricted to wandering around the circle. The linkage has six segments, OA and OC have a given length d (4/3 < d < 4), while AB, BC, CD, and DA all have length d/2; ABCD is a rhombus.

What is the locus of D as B moves around the circle?

[View the solution]

4 November 2014