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Math Help - Circumcircles meeting at a common point

  1. #1
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    Post Circumcircles meeting at a common point

    Hey i have this problem:

    Points D,E and F lie on the sides AB, BC and CA, respectively of triangle ABC.

    Prove that the circumcircles of triangles ADF, BED and CFE meet in a common point.

    Thanks
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let M be the point of intersection of the circumcircles of the triangles BDE and EFC. Then,

    \widehat{DME}=180-B

    \widehat{EMF}=180-C

    \widehat{DMF}=360-(180-B)-(180-C)=B+C=180-A

    That means M is on the circumcircle of the triangle ADF.
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