Question

o coarda ab a cercului a cercului C( O ,r) ,r=6 cm,are lungimea 6 cm.Daca M este un punct pe arcul mic ab ,aflati masura unghiului ∡ amb

Answer 1

Sper ca te-am ajutat! Mult noroc la scoala!

Answer 2

Răspuns:

$\boxed{\mathbf{m(\angle{AMB})=150^{\circ}}}$

Explicație pas cu pas:

$\mathbf{In\: cercul\: C(O\,;r)\: avem:}$

$\mathbf{AB=6\,cm\,(coarda)}$

$\mathbf{r=6cm \implies BO=AO=6\,cm}$

$\mathbf{In\: triunghiul\:\triangle\: AOB\: avem:}$

$\mathbf{AB=6cm\, , AO=6cm\,, BO=6cm \implies \triangle AOB-echilateral}$

$\mathbf{\triangle AOB-echilateral \implies \hat{A}=\hat{B}=\hat{O}=60^{\circ}}$

$\mathbf{\implies m(\widehat{AB})=60^{\circ}(unghi\:la\:centru)}$

$\mathbf{C(O\,;r)=360^{\circ}\implies \widehat{ANB}=360^{\circ}-60^{\circ}=300^{\circ} ,unde\:N \in C(O\,;r)\:si\: N \in ext\: \widehat{AB}}$$\mathbf{M \in \widehat{AB} \implies m(\angle {AMB})=\dfrac{\widehat{ANB}}{2}=\dfrac{300^{\circ}}{2}= \boxed{\mathbf{150^{\circ} }} }$