Geometry · Angle bisector · Isosceles triangle · Congruent triangles
Let \(CD\) be the bisector of the angle \(BCA\) of a triangle \(ABC\), where \(D\) lies on the side \(AB\), and suppose that
\[ AC + BD = BC + AD. \]
Prove that the triangle \(ABC\) is isosceles.
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Serbian Municipal Competition 2010, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source