Below is the illustration of the theorem (actually a corollary in the referenced book). Here $H$ is the internal center of similitude, $H_1$ is the external one, the theorem states that $IH$ bisects $\angle AIC$:. Here $H$ is the internal center of similitude, $H_1$ is the external one, the theorem states that $IH$ bisects $\angle AIC$:![enter image description here](