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Mathematical proof questions for senior high school entrance examination
Use similarity certificates. From the second question: BF = FD = EF+DE = 7, ∠ FBE = ∠ BAF, ∠ AFB = ∠ AFB, ∴△ BFE ∽△ AFB.

BF/AF=EF/BF, so BF? = AF ef, ∴ 49 = AF 4, so af =12.25 ∴ ad = af-df =12.25-7 = 5.25.