As shown in the figure, points a, B, D and E are on ⊙ o, and the extension lines of strings AE and BD intersect at point C. If AB is the diameter of ⊙ o, D is the midpoint of BC. Try to judge the size relationship between AB and AC, and give the proof Under the above conditions, what other conditions do △ ABC need to satisfy, and point e must be the midpoint of AC?

As shown in the figure, points a, B, D and E are on ⊙ o, and the extension lines of strings AE and BD intersect at point C. If AB is the diameter of ⊙ o, D is the midpoint of BC. Try to judge the size relationship between AB and AC, and give the proof Under the above conditions, what other conditions do △ ABC need to satisfy, and point e must be the midpoint of AC?

AB=AC．
The first method of proof is: 1
Connect ad
∵ AB is the diameter of ⊙ o,
∴AD⊥BC．
∵ ad is the common edge, BD = DC,
∴Rt△ABD≌Rt△ACD（SAS）．
∴AB=AC．
The second method of syndrome differentiation is as follows
Connect ad
∵ AB is the diameter of ⊙ o,
∴AD⊥BC．
And BD = DC, ad is the vertical line of BD
∴AB=AC．