Geometry Problem

Click the figure below to see the complete problem 650.

## Saturday, July 30, 2011

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## Saturday, July 30, 2011

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Geometry Problem 650: Tangent Circles, Diameter, Radius, Chord, Perpendicular

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Labels:
chord,
circle,
diameter,
metric relations,
perpendicular,
tangent

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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