$\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 }$

detailed solution

Correct option is C

Since the x-coordinates of two points A(2,5),B(2,7) are same, the line joining A,B is vertical line And since y-coordinates of two points B(2,7),C(1,7) are same. the line joining B,C is  horizontal line, so that the triangle ABC is right angled triangle with vertex at right angle is  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 Hence, the circum centre is S=2+12,5+72=32,6 The ortho centre is O(2,7)The slope of the line joining ortho centre and the circum centre is  mm=6−732−2=−1−12=2 If the inclination of any line θ then the slope of that line is m=tan⁡θ Here, tan⁡θ=2⇒θ=tan−1⁡(2) Therefore, the inclination of the line joining circum centre and ortho centre is tan−1⁡(2)