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March 30, 2017

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Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A line l through A intersects Γ1 and Γ2 at C and D, respectively. Let M be the midpoint of CD. The line MB intersects Γ1 and Γ2 again at E and F, respectively. If MA=129,MB=156 and MC=182, what is the value of EF?

  • circle geometry - ,

    I worked this earlier:

    29*182 = ME*156, so ME = 33.8333
    MD = MC = 129+182 = 311
    MF*156 = 129*311, so MF = 257.173
    EF = MF+ME = 33.833+257.173 = 291

    Is my answer incorrect?

  • circle geometry - ,

    Incorrect.

  • circle geometry - ,

    The correct answer is 301.
    Steve, in the first line is 129, not 29... and you shouldn't work with decimals because in the end the ugly dominator simplifies with the numerator.

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