Question

Daca pe cercul de centru O se gasesc punctele A, B, C, astfel incat AB = AC si masura arcului BC = 60 grade , atunci masura unghiului ABC  = ? ..la rasp da 75 grade

Answer 1

$m(arc~BC)=60 \textdegree \Rightarrow m(arc ~ BAC)=360 \textdegree -60 \textdegree=300 \textdegree.$

[AB]≡[AC] ⇒ $m(arc~AB)=m(arc~AC)= \frac{m(arc~BAC)}{2}= \frac{300 \textdegree}{2}=150 \textdegree. \\ \\ \ \textless \ ABC-unghi~inscris~in~cerc \Rightarrow m(\ \textless \ ABC)= \frac{m(arc ~AC)}{2} = \frac{150 \textdegree}{2}= \\ \\ =75 \textdegree.$