My attempt to prove the angle trisection identity of limaçons.
In the diagram below, I drew a limaçon trisectrix having polar equation $r=a+2a\cos\theta$ (In this case, $a=1$). Suppose $O(0,0), A(a,0), B(3a,0)$. Then, draw a line which has cartesian equation $y=kx\; (k\in \mathbb{R}^+)$ intersecting the limaçon at point $C$. Connect line $AC$.
Now, I'm supposed to prove $3\angle ACO=\angle BAC$. However, I got stuck. Is there a method without using analytic geometry?
