Question 23
Chords $AD,BC$ of circle $O$ meet at an interior point $P$. A circle $K$ lying in the region bounded by segments $AP,PC$ and circle $O$ is tangent to chords $AD,BC$ at $E,F$ respectively, and tangent to circle $O$ at $T$. Line $TF$ meets circle $O$ again at $G$, and $AG$ meets $EF$ at $I$.
Prove:
(1) $A,E,T,I$ are concyclic.
(2) $GB=GI$.
Prove:
(1) $A,E,T,I$ are concyclic.
(2) $GB=GI$.