### CGMO 2002/4

Posted:

**Sat Sep 30, 2017 12:02 pm**Circles $T_1$ and $T_2$ intersect at two points $B $ and $C$, and $BC$ is the diameter of $T_1$. Construct a tangent line to circle $T_1$ at $C$ intersecting $T_2$ at another point $A$. Line $AB$ meets $T_1$ again at $E $and line $CE $ meets $T_2$ again at $F $. Let $H $ be an arbitrary point on segment $AF $. Line $HE $meets $T_2$ again at $G $, and $BG $ meets $AC $ at $D $.

Prove that $$AH / HF=AC / CD $$

Prove that $$AH / HF=AC / CD $$