In square ABCD, point F is on ad, point E is on AB, AE = EB, AF = 1 / 4AD Connecting CE, EF (Pythagorean theorem, inverse theorem)

Method 1: AF ^ 2 + AE ^ 2 = EF ^ 2, be ^ 2 + BC ^ 2 = EC ^ 2, substitute AF = 1 / 4AD, AE = be = 1 / 2ad, BC = ad, then EF ^ 2 = 5 / 16ad ^ 2, EC ^ 2 = 5 / 4AD ^ 2, so EF ^ 2 + EC ^ 2 = 25 / 16ad ^ 2
Replace FD = 3 / 4AD by FC ^ 2 = FD ^ 2 + ad ^ 2, FC ^ 2 = 25 / 16ad ^ 2
So EF ^ 2 + EC ^ 2 = FC ^ 2, angle FEC = 90 degrees
Method 2: AF: EB = AE: BC = 1:2, angle a = angle B = 90 degrees, so triangle FAE is similar to triangle EBC, angle AEF = angle BCE. From angle BCE + angle CEB = 90 degrees, so angle AEF + angle CEB = 90 degrees, so angle CEF = 90 degrees

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