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AB + AC > = BC cos (<BAC) + 2AH sin(<BAC) , where AH altitude

Source: 2012 Indonesia MO Province P2 q4 OSP

December 10, 2020
geometrygeometric inequalityGeometric InequalitiesTrigonometric inequalitytrigonometry

Problem Statement

Given an acute triangle ABCABC. Point HH denotes the foot of the altitude drawn from AA. Prove that AB+AC≥BCcos∠BAC+2AHsin∠BACAB + AC \ge BC cos \angle BAC + 2AH sin \angle BAC
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