In the triangle ABC, ab = AC, angle BAC = 120 degrees, ad vertical BC, CD = 6, find the square of BD and AC (for the square of AC, and BD!)

In the triangle ABC, ab = AC, angle BAC = 120 degrees, ad vertical BC, CD = 6, find the square of BD and AC (for the square of AC, and BD!)

AB = AC, ad, vertical BC, triangle abd = triangle ACD, BD = CD = 6
Angle BAC = 120 degrees, angle c = 30 degrees, in a right triangle, the side opposite the angle of 30 degrees is equal to half of the hypotenuse. According to the Pythagorean theorem: the square of AD + the square of CD = the square of AC, let AC be a, the square of a = 6 + the square of half a, then the square of AC = 48