Let $ABC$ be a triangle with $∠A > ∠B$, prove that:
$BC > \frac 12AB$
2026-04-22 05:57:00.1776837420
Inequality in a triangle: $BC > \frac 12AB$ if $∠A > ∠B$ (self-answered)
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Since $∠A > ∠B$ then $BC>CA$ . Using the triangle inequality we obtain $AB<BC+CA$ and by the previous statement, $AB<2BC$ which gives: $BC > \frac 12AB$.