Find minimum value of the expression x^2 +y^2 subject to conditions Find the values of $x,y$ for which $x^2 + y^2$ takes the minimum value where $(x+5)^2 +(y-12)^2 =14$.
Tried Cauchy-Schwarz and AM - GM ,  unable to do.

Any point satisfying $\displaystyle(x+5)^2 +(y-12)^2 =14$ can be expressed as $\sqrt{14}\cos\phi-5,\sqrt{14}\sin\phi+12$ 
$\displaystyle x^2 + y^2=14(\cos^2\phi+\sin^2\phi)+2\sqrt{14}(12\sin\phi-5\cos\phi)+5^2+12^2$
$\displaystyle=14+12^2+5^2+2\sqrt{14}(12\sin\phi-5\cos\phi)$ 
This will attain minimum if $\displaystyle12\sin\phi-5\cos\phi$ is minimum
Now set $12=r\sin\phi,5=r\cos\phi$ to find $\displaystyle12\sin\phi-5\cos\phi=13\sin\left(\phi-\arctan\frac5{12}\right)$
What is the minimum value of $\displaystyle\sin\left(\phi-\arctan\frac5{12}\right)?$
