In the figure, if $A M$ is the perpendicular bisector of $C D$ , is equal to $A C - A B$ .

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Solution

The correct option is A BD
In $△ A D M$ and $A C M$ ,
AM=AM [Common side]
$∠ A M D = ∠ A M C$ [AM is perpendicular to CD]
$D M = M C$ [AM is the bisector of CD]

Hence, $△ A D M$ and $△ A M C$ are congruent... By SAS congruency
Therefore, $A D = A C$ [CPCT]
$\Rightarrow A B + B D = A C \Rightarrow B D = A C - A B$

Thus, the segment $B D$ is equal to $A C - A B$ .

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