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Kineska matura | Chinese Final Exam #2

Kružnice \omega_1 i \omega_2 sijeku se u B i C i neka je dužina BC promjer \omega_1. Tangenta u C kružnice \omega_1 siječe \omega_2 u A. AB siječe \omega_1 u E, a neka CE siječe \omega_2 u F. Neka je H točka na dužini AF. Neka HE siječe \omega_1 u G i neka se BG i AC sijeku u D. Nadalje, igrom slučaja ispalo je AD=420, AH=69, HF=43. Odredi duljinu dužine CD. Zaokružite rezultat na 6 decimala.
The circles \omega_1 and \omega_2 intersect at B and C. Let the segment BC be the diameter of \omega_1. The tangent of \omega_1 through point C meets \omega_2 at A. AB meets \omega_1 at E and CE meets \omega_2 at F. Let H be a point of the segment AF. HE and \omega_1 intersect at G, and BG and AC intersect at D. Coincidentally, it turns out AD = 420, AH = 69, HF = 43. Determine the length of the segment CD. Round the result to 6 decimal places.