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# Plane Geometry watch

1. 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.
2. (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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