Visual representation of chordal metric in $\mathbb{P}^1(\mathbb{C})$

Question

I am reading a book and they are using the cordal metric in $\mathbb{P}^1(\mathbb{C})$ defined as:

$\rho(P_1,P_2)= \frac{\mid X_1Y_2 - X_2Y_1 \mid}{\sqrt{\mid X_1^2\mid+\mid Y_1^2 \mid}\sqrt{\mid X_2^2\mid+\mid Y_2^2 \mid}}$

for $P_i=(X_i,Y_i)$.

Can anyone give me a visual representation or explanation of what this metric measures? I guessed arc lenght but the lack of trigonomic functions in the metric quickly changed my mind.