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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?

  • geometry -

    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

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