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.

Notations:

$\gcd(\cdot)$ denotes the greatest common divisor function.
$| \cdot |$ denotes the absolute value function.

Because dydx \frac{dy}{dx}dxdy​ has killed all the creativity inside!

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