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March 27, 2017

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Let AB be the diameter of circle Γ1. In the interior of Γ1, there are circles Γ2 and Γ3 that are tangent to Γ1 at A and B, respectively. Γ2 and Γ3 are also externally tangent at C. This exterior tangent cuts Γ1 at P and Q, with PQ=20. The area that is within Γ1 but not in Γ2 or Γ3 is equal to Mπ. Determine M.

  • Math - ,

    10

  • Math - ,

    wrong

  • Math - ,

    should be 26

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    WRONG!!!

  • Math - ,

    wrong dr.cao.....

  • Math - ,

    wrong de.cao

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    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....
    wrong dr.cao.....

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    calm down dr.cao 3rd
    calm down

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    Dude don`t fight please tell the answer

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    50
    Let the radius of larger circle be a, smaller ones be 'b' and 'c'.
    Ans = pie(a^2-(b^2+c^2)) here we are only concerned with (a^2-(b^2+c^2))=
    (a^2 - ((b + c)^2 - 2bc) = 2bc as a=b+c
    Using intersecting chord theorem,
    2bc= AC*BC/4= PC*CQ/4= 10*10/4 as diameter bisects chord
    = 50 Ans

  • Math - ,

    SORRY GUYS I MEANT TO SAY ITS 60 SORRY DON'T USE 50 ITS 60!!

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