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Answer:
(a) no
(b) no
Explanation:
The two questions are asking essentially the same thing. There is nothing that indicates DC ≅ DB or that AC ≅ AB. One (both) of these conditions is (are) required for ΔBAC to be isosceles, so that AD is both a perpendicular bisector of BC and a bisector of angle BAC.
There is not enough information to answer either question affirmatively.