Tuesday, March 10, 2015

Problem 1095: Externally Tangent Circles, Common Tangent, Radius, Geometric Mean, Metric Relations

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

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Online Math: Geometry Problem 1095: Externally Tangent Circles, Common Tangent, Radius, Geometric Mean, Metric Relations.

Posted by Antonio Gutierrez at 5:02 PM
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3 comments:

  1. PravinMarch 11, 2015 at 12:56 AM

    d1 / r1 = d2 / r2 = (d1 - d2) / (r1 - r2)

    ={sqrt[(r1 + r2)^2 - (r1 - r2)^2]} / (r1 - r2)

    = 2sqrt(r1.r2) / (r1 - r2)

    from which the result follows.

    ReplyDelete
  2. Jacob HA (EMK2000)March 11, 2015 at 5:45 AM

    Let x=O₂P.

    r₁/r₂ = (r₁+r₂+x)/x = 1 + (r₁+r₂)/x
    x = r₂(r₁+r₂)/(r₁-r₂)

    d₂² = x² - r₂²
    = r₂² (4r₁r₂)/(r₁-r₂)²

    d₂ = 2r₂ √(r₁r₂) / (r₁ - r₂)

    d₁/d₂ = r₁/r₂
    d₁ = 2r₁ √(r₁r₂) / (r₁ - r₂)

    ReplyDelete
  3. ion raduMarch 18, 2015 at 11:21 AM

    A₁A₂² =(r₁+r₂)²- (r₁-r₂)²=4r₁r₂=>d₁-d₂= 2 √(r₁r₂)
    d₁/d₂ = r₁/r₂=>d₁/(d₁-d₂)=r₁/(r₁-r₂)=>d₁ = 2r₁ √(r₁r₂) / (r₁ - r₂);d2/(d₁-d₂)=r2/(r₁-r₂)=>d₂ = 2r₂ √(r₁r₂) / (r₁ - r₂)

    ReplyDelete

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