It is known that AB=AC, ∠BAC=α.

Therefore ∠ ABC = ∠ ACB = (180-α)/2 = 90-(α/2).

Known ∠ CBD = 60.

So ∠ Abd = ∠ ABC-∠ CBD = [90-(α/2)]-60 = 30-(α/2).

(2)

Connecting CD, AD

Known BD = BC∠CBD = 60.

So △BCD is an equilateral triangle.

So BD=CD, ∠ BCD = ∠ CBD = 60.

So, ∠ABD=∠ACD

Known AB=AC

So △ Abd△ ACD (SAS)

So, ∠BAD=∠CAD

That is, AD is the bisector of the isosceles △ABC vertex angle.

So AD divides BC vertically.

(3)

Connect AD and CD as shown in the figure.

Turn left | turn right

Given that △ABE is an equilateral triangle, then: ∠ Abe = 60, AB=EB.

It is proved from the above formula (2) that △BCD is an equilateral triangle.

Then, ∠ DBC = 60, BD=BC.

Therefore ∠ Abd = ∠ EBC = 60-∠ DBE.

So △ Abd△ EBC (SAS)

Therefore, ad = ce Asian Development Bank = ∠ European Central Bank.

Proved by (2) ∠ADC=∠ADB