The following construction was made: 1. We constructed the circumcircle of the triangle ABC. 2. We constructed the three altitudes AG, BE and CF and extended them to intersect the circumcircle at points D, E and F. 3. Determine the ratios AD:AG , CF:CI and BE:BJ. Discovery! AD/AG+CF/CI+BE/BJ=4 See the proof of this fact here. 

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