MHB Finding Angle C in Triangle ABC

[Albert1]

$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\
find \,\, \angle C=?$

 

[Albert1]

$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\
find \,\, \angle C=?$

hint

Spoiler

prove $\angle A=2\angle C$

 

[Albert1]

$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}---(1)\\
find \,\, \angle C=?$

more hint:

Spoiler

in fact $\angle B=30^o$ is not important, you should prove for any triangle if $\angle A=2\angle C $ then (1) will meet

 

[Albert1]

more hint:

Spoiler

in fact $\angle B=30^o$ is not important, you should prove for any triangle if $\angle A=2\angle C $ then (1) will meet

my solution :

Spoiler

View attachment 5446