First of all, I think there is no need of BC in the sum.
We know that the diagonals of a rectangle are equal in length. Thus, BD = AC = 13 cm 

Now, we can see that AC is the radius of the circle and the length of AC is 13cm
Therefore, diameter of the circle = 13 x 2
= 26cm

Hope that helps !!
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Plz pick it as best if it was helpful !! :)