# Lengthy, Lengthier, Lengthiest!

Geometry Level 3

Consider a circle $$\Omega(x,y): x^2+y^2-6x-12y-405=0$$ . Let $$P \equiv (13,26)$$.Let $$t_1 , t_2$$ be the tangents from $$P$$ to $$\Omega$$ . Let $$t_1 , t_2 \cap \Omega =\{A,B\}$$ respectively . If $$A \equiv (x_{A} , y_{A} ) , B \equiv (x_{B} , y_{B})$$ ,

Find $$x_{A} + y_{A}+x_{B} + y_{B}$$.

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