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Angle Bisector

This is how to create an Angle Bisector, by using circles and intersections. You can prove that this construction works by ITT (with triangles ADE and AEF) and SAS ( with triangles ADF and AEF), these triangle theorems show Triangle ADF is congruent to Triangle AEF, and so by CPCTC, we know that the angles (alpha and beta) are the same. Showing that AF is indeed the bisector of angle A.