# The triplets - 5, 12, 13

Geometry Level 4

Let $$A(5,12)$$, $$B(-13\cos { \theta } ,13\sin { \theta } )$$ and $$C(13\sin { \theta } ,-13\cos { \theta } )$$ are angular points of $$\triangle ABC$$ where $$\theta \in \Re$$. The locus of the orthocentre of the $$\triangle ABC$$ is $$ax+by+c=0$$ where $$a,b,c$$ are integers. Find the minimum positive value of $$a+b+c$$.

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