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February 10th, 2018, 02:54 AM  #11 
Newbie Joined: Dec 2017 From: Spain Posts: 15 Thanks: 1 
Sorry I didn't answer The trick is using three theorems: Tales theorem Altitudes theorem in rectangle triangles and remember that the product of the altitudesparts is always equal: AH*HHa=BH*HHb=CH*HHc Hence all the lines HPa; HQa; HPb; HQb; HPc; HQc have the same length and origin (H). Hence they are all radii of a common circle 

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circles, cyclic hexagon, exercise, geometry, involved, orthocenter, parallels 
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