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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We are asked to find the length of the segment $AC.$ Let's consider the diagram below.

As we can see, the segment $AC$ consists of two segments: $AD$ and $DC.$ Thus, by the Segment Addition Postulate, its length equals the sum of these segments lengths.
$AC=AD+DC $
The measure $AD$ is known from the diagram. How can find the measure of $DC?$ From the diagram, we see that segments $AB$ and $BC$ have the same length. This means, point $B$ is equidistant form $A$ and $C.$ Let's now use the Converse of the Perpendicular Bisector Theorem.
$If a point is equidistantfrom the endpoints of a segment,then it is on the perpendicular bisectorof the segment. $
According to the theorem, $BD$ is a perpendicular __bisector__ of the segment $AC.$ Therefore, $D$ is a midpoint of $AC.$ We conclude that the measure of $DC$ is also $3.5.$ Finally, we can substitute $AD$ with $3.5$ and $DC$ with $3.5$ in the above equation, and calculate $AC.$
$AC=3.5+3.5=7 $