$\text{ The points }(2,5),(2,7),(1,7)\text{ forms a triangle. The inclination of the line joining the }$$\text{ ortho centre and the circum centre of the triangle is }$

$\text{ Since the }x\text{-coordinates of two points }A(2,5),B(2,7)\text{ are same, the line joining }A,B\text{ is vertical line}$

$\text{ And since }y\text{-coordinates of two points }B(2,7),C(1,7)\text{ are same. the line joining }B,C\text{ is }$

$\text{ horizontal line, so that the triangle }ABC\text{ is right angled triangle with vertex at right angle is }$$\text{ at }B(2,7)$

In right angled triangle, the ortho centre is vertex at right angle and the circum centre is midpoint of the hypotenuse

$\text{ Hence, the circum centre is }S=\left(\frac{2+1}{2},\frac{5+7}{2}\right)=\left(\frac{3}{2},6\right)$

$\text{ The ortho centre is }O(2,7)$

The slope of the line joining ortho centre and the circum centre is  m

$\begin{array}{c}m=\frac{6-7}{\frac{3}{2}-2}\\ =\frac{-1}{-\frac{1}{2}}\\ =2\end{array}$

$\text{ If the inclination of any line }\theta \text{ then the slope of that line is }m=\tan \theta$

$\text{ Here, }\tan \theta =2\Rightarrow \theta ={\tan }^{-1}\left(2\right)$

$\text{ Therefore, the inclination of the line joining circum centre and ortho centre is }{\tan }^{-1}\left(2\right)$