Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemClick the figure below to see the complete problem 650.
http://img839.imageshack.us/img839/9798/problem649.pngAO cut circle C1 at E . Connect OC and EB ( see picture)In right triangle OCA we have AC^2=AO.AD = 1 ( relation in a right triangle)In right triangle ABE we have AB^2=AE.AD=2.AO.AD= 2So AB=SQRT(2)Peter Tran
Let AB intersect C2 at EOE ⊥ AB and so O,B,E,D are concyclicAlso OE bisects AB, AD = x/2⊿ADB ~ ⊿AEOAD/AE = AB/AOAB.AE = AD.AO =AC 2 = 1x.x/2 = 1,x2 =2, x =√2