Saturday, July 30, 2011

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

Geometry Problem
Click the figure below to see the complete problem 650.


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

Posted by Antonio Gutierrez at 7:27 AM
Labels: , , , , ,

2 comments:

  1. Peter TranJuly 30, 2011 at 7:59 AM

    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

    ReplyDelete
  2. PravinJuly 31, 2011 at 10:07 AM

    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

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