Saturday, May 28, 2011

Problem 607: Intersecting Circles, Triangles, Metric Relations, Measurement

Geometry Problem
Click the figure below to see the complete problem 607.

Problem 607: Intersecting Circles, Triangles, Metric Relations, Measurement.

Posted by Antonio Gutierrez at 10:24 AM
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2 comments:

  1. PravinMay 30, 2011 at 6:53 PM

    Isosceles triangles ACF, BCE are similar.
    CF/CE = AC/BC
    CF.CB = CE.CA, and so A,B,F,E are concyclic.
    GBA, GFE are secants from G to the circle BAEF.
    GB.GA = GF.GE,
    x(x+10)= (8).(12),
    (x + 5)² = 121,
    x+5=11, x=6

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  2. Sumith PeirisFebruary 1, 2016 at 3:56 AM

    < BEC = < BCE = < AFC

    Hence BAEF is cyclic

    So 8 x 12 = x(x+10)

    Solving the quadratic for positive x

    x = 6

    Sumith Peiris
    Moratuwa
    Sri Lanka

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