As shown in the figure, in the known RT △ ABC, the ⊙ o cross bevel BC with ab as the diameter is at point D, and E is the midpoint of AC. connect ed and extend the extension line of intersection AB at point F. (1) prove that De is the tangent of ⊙ o; (2) if ⊙ f = 30 ° AB = 4, find the length of DF and ef

As shown in the figure, in the known RT △ ABC, the ⊙ o cross bevel BC with ab as the diameter is at point D, and E is the midpoint of AC. connect ed and extend the extension line of intersection AB at point F. (1) prove that De is the tangent of ⊙ o; (2) if ⊙ f = 30 ° AB = 4, find the length of DF and ef

(1) It is proved that: connecting BD, do, ∵ AB is the diameter of ⊙ o, ∵ CE = EA, ∵ 1 = 4. ∵ od = OA, ∵ 2 = 3. ∵ 1 + 2 = 3 + 4 = 90 °, that is, ∵ Edo = 90 ° and ∵ od is the radius, and ∵ De is the tangent line of ⊙ O. (2) from (1), ∵