http://img839.imageshack.us/img839/9798/problem649.png AO 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= 2 So AB=SQRT(2) Peter Tran
Let AB intersect C2 at E OE ⊥ AB and so O,B,E,D are concyclic Also OE bisects AB, AD = x/2 ⊿ADB ~ ⊿AEO AD/AE = AB/AO AB.AE = AD.AO =AC 2 = 1 x.x/2 = 1, x2 =2, x =√2
http://img839.imageshack.us/img839/9798/problem649.png
ReplyDeleteAO 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= 2
So AB=SQRT(2)
Peter Tran
Let AB intersect C2 at E
ReplyDeleteOE ⊥ AB and so O,B,E,D are concyclic
Also OE bisects AB,
AD = x/2
⊿ADB ~ ⊿AEO
AD/AE = AB/AO
AB.AE = AD.AO =AC 2 = 1
x.x/2 = 1,
x2 =2,
x =√2