# Length of a line in an isosceles triangle. (mind boggling )

In an isosceles $\triangle ABC$, side $AB$ and $AC$ are equal in length. There exists a point $D$ on the side $AB$. $\angle BAC$ is $\theta$. The side $AD$ is $2$ units smaller than $AC$. What is the generalized formula to calculate the side $CD$?

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I have tried this thing. I think that the formula would require some simple trignometry. –  Vinay - mathematician. May 28 '14 at 15:38
BD can be anything. –  mercio May 28 '14 at 15:41
yes bd can be anything. –  Vinay - mathematician. May 28 '14 at 15:50
Use the Law of Cosines –  Graham Kemp May 28 '14 at 16:01
I am asking for a proof in an algebraic form. Well I have also applied the law of cosines –  Vinay - mathematician. May 28 '14 at 16:02

This is a simple application of the cosine rule to the triangle $ACD$
$$CD^2=(a-2)^2+a^2-2a(a-2)\cos\theta$$
You can draw a picture to convince yourself that the length of $BD$ does not depend on $\theta$. You will need to be given more information.