Wednesday, November 26, 2014

Geometry Problem 1063: Triangle, Orthocenter, Altitudes, Equal Product of the Lengths of Segments

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Online Math: Geometry Problem 1063: Triangle, Orthocenter, Altitudes, Equal Product of the Lengths of Segments.

Posted by Antonio Gutierrez at 9:40 AM
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2 comments:

  1. Jacob HA (EMK2000)November 26, 2014 at 4:43 PM

    Since ABA₁B₁ is concyclic, with AB as diameter,
    AA₁ and BB₁ are two chords intersecting at H,
    thus AH×HA₁ = BH×HB₁.

    Similarly consider cyclic quadrilateral BCB₁C₁,
    we have BH×HB₁ = CH×HC₁.

    Hence, AH×HA₁ = BH×HB₁ = CH×HC₁.

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  2. ion raduNovember 30, 2014 at 1:37 AM

    triunghiul ANB1este asemenea cu triunghiul BHA1,BHC1~CHB1 (UU)=>AH/BH=HB1/HA1;HB/HC=HC1/HB1 => AH×HA₁ = BH×HB₁ = CH×HC₁.

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