Assume for \(\triangle {ABC}\), \(X, Y, Z\) are defined as \(X \in \overline {AB}\), \(Y \in \overline {BC}\), and \(Z \in \overline {CA}\). Then, the following equation of cross-ratio holds. \[ \frac {XA}{XB} \cdot \frac {YB}{YC} \cdot \frac {ZC}{ZA} = -1 \]