The distance of the center of the circle $x^2+y^2=2x$ from the common chord of the circles $x^2+y^2+5x-8y+1=0$ and$x^2+y^2-3x+7y-25=0\text{, is }$

The common chord of the circles $S=0$ and 

$S^{\mathrm{\prime }}=0\text{ is }S-S^{\mathrm{\prime }}=0$

$\therefore x^2+y^2+5x-8y+1-\left(x^2+y^2-3x+7y-25\right)=0$              

$\Rightarrow 8x-15y+26=0$                                                  ..(i)

The centre of $x^2+y^2-2x=0\text{ is }(1,0)$

The distance of (1, 0) from (i) is 

$\frac{8+26}{\sqrt{8^2+{15}^2}}=\frac{34}{17}=2$