Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 700.
http://img37.imageshack.us/img37/9728/problem700.pngFD cut AB and AO at G and H ( see picture)Note that AD=AG=DG=6OA= AG*2/√3 =12/√3In triangle OHF , applying Pythagoras Theorem we get HF=3. √5So x=HF-HD=3(√5-1)Peter Tran
Extend ED to cut AC at X and circle at YEDXY ∥ ABSo DE = 6 ; and XY = x (by symmetry) ED.DY = AD.DCx(6 + x) = 36x²+ 6x = 36(x + 3)² = 45x = 3(√5 - 1)