Question

Intr-un triunghi ABC , m(unghiului ABC) =60 grade si AB=2 x BC . Afla masura unghiului ACB

Answer 1

$\rm Luam~M-mijlocul~segmentului~[AB]. \\ \\ BM=MA=BC. \\ \\ BM=BC \Rightarrow \Delta BMC-isoscel,~dar~m(\ \textless \ ABC)=60 \textdegree \Rightarrow \\ \\ \Rightarrow \Delta BMC-echilateral \Rightarrow BM=MC=BC. \\ \\ Cum~BM= \frac{AB}{2} ~si~BM=MC \Rightarrow MC= \frac{AB}{2} \Rightarrow m(\ \textless \ ACB)=90 \textdegree.$