AD for triangle ABM is both median and height. And this is the property of the median for an isosceles triangle. Therefore, the triangle ABM is isosceles with the base BM.
By the definition of an isosceles triangle, AB = AM.
Because BM is the median for triangle ABC, therefore AM = MC (as defined by the median).
Then AC = AM * 2. As we found out earlier, AM = AB => AC = AB * 2 = 3 * 2 = 6.
Answer: AC = 6.
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