A straight line through the origin intersects the curve $C_1: r=1+\cos(t),\, 0 \leq t \leq 2\pi$ at two points $P_1$ and $P_2$ outside of the origin. Show that the distance between $P_1$ and $P_2$ is $2$.
How do I go about solving this problem? All I can think of is having $P_1=(0,0)$ and $P_2=(0,2)$ but if I understand the description of this question correctly then this isn't valid. Anyone know how to go about this one?
Hint: A line passing through the origin at an angle of $\theta_0$ is described in polar form as those points with $r>0$ and either $\theta=\theta_0$ or $\theta=\theta_0+\pi$.