Because $$\frac{dy}{dx}$$ has killed all the creativity inside!

Geometry Level 3

As shown in the figure, a circle centered at $$O=(3,5)$$ bears a point $$P=(8,11)$$ hosting a line tangent to the circle. Can you find out the equation of that tangent line without using calculus?

If the equation of the line can be expressed in the form $$ax+by+c=0$$, where $$a$$,$$b$$ and $$c$$ are integers and $$\gcd(a,b,c)=1$$, then enter $$|abc|$$ as your answer.

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