Monday, January 11, 2010

Problem 417: Tangent circles, Tangent lines, Angles

Proposed Problem
Click the figure below to see the complete problem 417 about Tangent circles, Tangent lines, Angles.

Problem 417: Tangent circles, Tangent lines, Angles.
See also:
Complete Problem 417
Level: High School, SAT Prep, College geometry

4 comments:

  1. join E to A, D to B
    draw DH perpendicular to EA

    in ABDH
    ang( HAB+ABD+BDH+DHA)= 164 + BDH + 90 (HAB+ABD=2∙82)
    => ang BDH = 106
    => ang HDF = 164

    => x = 16

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  2. solution needs to be improved
    how did u get HAB + ABD = 2.82

    ReplyDelete
  3. thanks, I saw it today

    ang ECD = 1/2 ( arc EC + arc CD ) (build common tang)

    ang EAC + ang CBD = arc EC + arc CD

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  4. Problem 417
    I design the common external tangent of two circles intersecting tinEF
    in point K and DF intersects the KC at the point M. If <MCD=a=<MDC, then <KMF=2a.
    But <KCE=82-2a=<KEC, so <FKC=184-2a.Then x+2a+184-2a=180 therefore x=16.
    APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE

    ReplyDelete