Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to enlarge the problem 951.
2(180°−∠EAD)=2∠AFE=∠AOE=∠OAC=90°−∠CAD=∠QAD=∠AQG=2∠AHG=2∠DAHThus, E,A,H are collinear. Similarly, F,A,G are collinear. By the above argument, ∠EFG=∠EFA=∠AHG=∠EHGHence, F,E,H,G concyclic.
<CEA=<DGA=<CAD. <DAH=45-<CAD/2, and <EAD=90+<CAD+(45-<CAD/2), so <EAD+<DAH=180 and EAH are collinear. Same reasoning for FAG to be collinear. Then <EFG=<EHG=45-<CAD/2.