An Incenter Sum

★ 7/10plane geometry Law of Sines trigonometry Trigonometric Identities Triangle Geometry

Problem

In $\triangle ABC$ (usual notation),

(a\cos C + c\cos A)\tan A = \sqrt3\,b.

1. Find $A$ . 2. If $a = \sqrt3$ and $I$ is the incenter, find the maximum of $IB + IC$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Law of Sines, trigonometry, Trigonometric Identities, Triangle Geometry

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