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As shown in the figure, ⊙ o is the circumscribed circle of ⊙ ABC, FH is the tangent of ⊙ o, the tangent point is f, FH ∥ BC, the bisector BD connecting AF to e, the bisector BD connecting AF to D, connecting BF. (1) prove that AF bisects ∠ BAC; (2) prove that BF = FD; (3) if EF = 4, de = 3, find the length of AD
(1) FH is the tangent of \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\and, In △ BFE and △ AFB, ∵ BDF = ∵ FBD, ∵ BF = FD (6 points) (3) in △ BFE and △ AFB, ∵ 5 = ∵ 2 = ∵ 1, ∵ AFB = ∵ AFB, ∵ BFE ∵ AFB (7 points) ∵ bfaf ∵ fefb, (8 points) ∵ BF2 = Fe ∵ FA = bf2fe (9 points), EF = 4, BF = FD = EF + de = 4 + 3 = 7, ∵ FA = 724 = 494 ∵ ad = af-df = af - (de + EF) = 494 − 7 = 214 (10 points)
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