Monday, May 17, 2010

Problem 456: Three tangent circles, Center, Chord, Secant, Collinear

Geometry Problem
Click the figure below to see the complete problem 456 about Three tangent circles, Center, Chord, Secant, Collinear.

Problem 456: Three tangent circles, Center, Chord, Secant, Collinear.
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Complete Problem 456

Level: High School, SAT Prep, College geometry

Posted by Antonio Gutierrez at 3:28 PM
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2 comments:

  1. c .t . e. oMay 18, 2010 at 1:03 AM

    B, E, C are collinear (from E, EB, EC perpen to comm tg)
    BDE = BED , ADG = AGD ( DB = BE = r, AD = AG = R )
    =>
    BED = AGD => BEC//AG (1)

    CFE = CEF , AFH = AHF ( CE = CF = r, AH = AF = R )
    =>
    CEF = AHF => BEC//AH (2)
    from (1) & (2)
    from A we can draw just one parallel to a line (BEC)

    H, A, G are collinear
    -----------------------------------------

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  2. APOSTOLIS MANOLOUDISJune 19, 2016 at 4:09 PM

    Problem 456
    Design all common external tangents intersect at P.(P is the radical center of three circles).
    Is <DAH=2.<DFH=2.<DFE=<DPE, (PD=PE=PF), <FAG=2.<FDG=2.<FDE=<FPE and <DAF=
    180-<DPF (ADPF=cyclic).Then <DAH+<FAG+<DAF=<EPD+<EPF+180-<DPE=180.
    Therefore H,A and G are collinear.
    APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE

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