CEMC Cayley, 2007

Geometry Difficulty 2.0 Junior Find the answer Canada

In the diagram, triangles $ABC$ and $CBD$ are isosceles. The perimeter of $\triangle CBD$ is $19$ , the perimeter of $\triangle ABC$ is $20$ , and the length of $BD$ is $7$ . What is the length of $AB$ ?

(A) $5$ (B) $6$ (C) $7$ (D) $8$ (E) $9$

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