Second question, is there a problem, a? +b? =c? And because △ABC is a singular triangle and b > a.
So c? +a? =2b?
So 2a? =b?
So a: b: c = 1: √ 2: √ 3.
The third question: ① Because AB is the diameter of a circle.
So AC? +BC? =AB?
AD? +BD? =AB?
It is also known from the question that d is the midpoint of a semicircle.
So AD=BD
So AC? +BC? =2AD?
Because BC=CE, AD=AE.
So AC? +CE? =2AE?
So △ACE is a singular triangle.
② If △ACE is a right triangle.
So AC? +AE? =CE? Or CE? +AE? =AC?
According to the second question,
Ac: AE: ce = 1: √ 2: √ 3 or ce: AE: AC = 1: √ 2: √ 3.
So AC: CB = 1: √ 3 or √ 3: 1.
So ∠AOC=60? Or 120?