Sunday, February 8, 2015

Geometry Problem 1080: Square, Circle, Tangent, Side, Radius, 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 1080: Square, Circle, Tangent, Side, Radius, Metric Relations.

Posted by Antonio Gutierrez at 10:41 AM
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2 comments:

  1. Jacob HA (EMK2000)February 8, 2015 at 7:41 PM

    √2 a = AC
    = AH + HO + OC
    = √2 GH + HO + √2 HO
    = 2√2 HO + HO + √2 HO
    = (3√2 + 1)HO

    HO = √2 a / (3√2 + 1) = (6 - √2)a/17
    EF = 2(1+√2)(6 - √2) a/17 = 2a (4+5√2)/17

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  2. Peter TranFebruary 8, 2015 at 10:18 PM

    http://s21.postimg.org/us94eayo7/pro_1080.png
    Let MD=y and OH=r
    We have y= r+r/√2
    Or r=2.y/(2+√2)
    We have 2.r= GH= a-y
    So 4.y/(2+√2)= a-y => y= a/(1+4/(2+√2))
    EF=2.y√2= (4+4√2).a/(6+√2)
    So EF=2.a*(4+5. √2)/17

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