Question

In triangle ABC, 2(AB X AB) = AC X AC. Find angle B.

Answer 1

$Look\ at\ the\ picture.\\\\\angle B=\alpha\\\\2(|AB|\times|AB|)=|AC|\times|AC|\\\\2|AB|^2=|AC|^2\\\\|AC|^2=2|AB|^2\\\\|AC|^2=|AB|^2+|AB|^2\\\\|AC|^2=|AB|^2+|AB|^2-2\times|AB|\times|AB|\times0\\\\\underbrace{|AC|^2=|AB|^2+|AB|^2-2\times|AB|\times|AB|\times cos90^o}_{Law\ of\ cosines}\\\\Answer:|\angle B|=90^o\to\Delta ABC\ is\ right\ triangle.$