Кто возглавлял «Южное общество» декабристов?

ответ - П. Пестель

АЕ = ЕС ⇒ ∠ЕАС = ∠ЕСА, обозначим их α.
Пусть АВ = а, тогда АС = 2а.
Биссектриса делит противолежащую сторону на отрезки, пропорциональные прилежащим сторонам. Тогда
ВЕ:ЕС = АВ:АС = 1:2
Пусть ВЕ = х, тогда ЕС = EA = 2х.
В ΔЕАС по теореме косинусов для угла ЕАС:
cosα = (AE² + AC² - EC²)/(2AE·AC)
cosα = (4x² + 4a² - 4x²)/(8ax) = a/(2x)
В ΔВАЕ по теореме косинусов для угла ВАЕ:
cosα = (AB² + AE² - BE²)/(2AB·AE)
cosα = (a² + 4x² - x²)/(4ax) = (a² + 3x²)/(4ax)
(a² + 3x²)/(4ax) = a/(2x)
a² + 3x² = 2a²
a² = 3x²
a = x√3
cosα = a/(2x) = x√3/(2x) = √3/2 ⇒ α = 30°
∠ВСА = 30°
∠ВАС = 60°  ⇒  ∠АВС = 90°

I have been to London, England.
I was there two years ago.
I stayed in a hotel.
I travelled with my family.
I visited a lot of interesting places there.
I saw Tower of London and Westminster Abbey and went to the
British Museum.
My favourite sight is Buckingham Palace.
I like it because it is very beautiful and it has a lot interesting
traditions.
I had a good time in London.
The best day of the trip was when T rode on London Eye.
My favourite souvenir is a cup of London sights.
I bought it at the exhibition.
I'm going to visit this city once more.
I think I'11 have good impressions.