An Angle Bisector Minimum

★ 6/10plane geometry Law of Sines trigonometry Law of Cosines AM-GM inequality

Problem

In triangle $ABC$ , the sides opposite angles $A, B, C$ are $a, b, c$ , and

(a + b)(\sin A - \sin B) = c(\sin C + \sin B).

If the bisector $AD$ of angle $A$ has length $2$ , find the minimum value of $4b + c$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Law of Sines, trigonometry, Law of Cosines, AM-GM, inequality

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