Height Equals Excess

★ 7/10plane geometry trigonometry Trigonometric Identities AM-GM Triangle Geometry

Problem

In triangle $ABC$ , the sides opposite angles $A, B, C$ are $a, b, c$ , the altitude to side $BC$ has length $h$ , and

b + c = a + h.

1. If $h = \dfrac{2}{3}a$ and $k\sin A - \cos A = 1$ , find the real number $k$ . 2. Find the minimum value of $\tan A$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, trigonometry, Trigonometric Identities, AM-GM, Triangle Geometry

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