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    Let ABC be a triangle, and extend the sides AB and AC. Suppose that the bisectors of
    the two exterior angles at B and C of the triangle meet in point D, and draw a line from D
    perpendicular to AB which meets AB in E. Prove that AE =
    1
    2
    (AB + BC + CA).
    Hint: Draw a line from D perpendicular to BC which meets BC in F and a line from D
    perpendicular to AC which meets AC in G. Then add the line segment AD.
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    (Original post by Maryam Farid)
    Let ABC be a triangle, and extend the sides AB and AC. Suppose that the bisectors of
    the two exterior angles at B and C of the triangle meet in point D, and draw a line from D
    perpendicular to AB which meets AB in E. Prove that AE =
    1
    2
    (AB + BC + CA).
    Hint: Draw a line from D perpendicular to BC which meets BC in F and a line from D
    perpendicular to AC which meets AC in G. Then add the line segment AD.
    What have you tried?
 
 
 
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Updated: February 7, 2018
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