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.
by
Arkajyoti Banerjee