Monday, February 17, 2014

Geometry Problem 985: Circle, Radius, Perpendicular, Concentric Circles, Congruence, Triangle

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

Click the figure below to see the complete problem 985.

Online Geometry Problem 985: Circle, Radius, Perpendicular, Concentric Circles, Congruence, Triangle

Posted by Antonio Gutierrez at 4:17 PM
Labels: , , , , ,

3 comments:

  1. Jacob HA (EMK2000)February 17, 2014 at 5:26 PM

    1. CD/OA = EG/OF
    2. CD/OA = CD/OB = CE/OE = AF/OF

    Thus, AF=EG.

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  2. PravinFebruary 19, 2014 at 12:41 AM

    Let R, r denote the radii of the outer and inner concentric circles.
    Now EG / r = EG / OB = DG / OD = EG / OB = CE / OC = AF / r
    since AF = OF - OA = R - r = OE - OC = CE.
    Hence EG = AF

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  3. Sumith PeirisFebruary 12, 2020 at 9:29 PM

    If R and r are the radii of the larger and smaller circles respectively, then from similar triangles,

    R/OG = r/OD = EG/DG

    Hence EG = r.(DG/OD) = r. (OG-OD)/OD = r.(OG/OD - 1) = r.(R/r - 1) = R-r = AF

    Sumith Peiris
    Moratuwa
    Sri Lanka

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