# Triple Circles, but actually, there is only one

Geometry Level 4

Circle $$\omega_1$$ is tangent to $$AB$$ and $$AC$$, $$\omega_2$$ is tangent to $$BA$$ and $$BC$$, and $$\omega_3$$ is tangent to $$CB$$ and $$CA$$. Those three circles have equal radii and are inside $$\triangle ABC$$. If $$\omega_1, \omega_2$$ and $$\omega_3$$ have a common point $$P$$, which of the answers is true?

$$\textbf{Note:}$$ $$I$$ is the incenter. $$O$$ is the circumcenter, $$H$$ is the orthocenter, $$G$$ is the centroid, $$I_a$$ is the excenter for the A-excircle, and $$A' , B', C'$$ are the centers of circles $$\omega_1, \omega_2 , \omega_3$$ respectively.

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