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

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) It is proved that the connection of of ∵ FH is the tangent of ⊙ o ∵ of ⊥ FH (1 point) ∵ FH ∥ BC, ∵ of vertical bisection BC (2 points) ∵ BF = FC, ∵ 1 = ∵ 2, ∵ AF bisection ∵ BAC (3 points) (2) it is proved that from (1) and the conditions, we can know ∵ 1 = ∵ 2, ∵ 4 = ∵ 3, ∵ 5 = ∵ 2 (4 points) ∵ 1 + ∵ 4 = ∵ 2 + ∵ 3