Finding Radical centre problem

Question

Suppose 3 circles are drawn taking the 3 sides of a triangle as their diameters, what would be the radical centre of these circles? The options are circumcenter, orthocenter and incenter Any help would be appreciated

Answer 1

We can prove that by considering a triangle ABC with known coordinates of A , B and C. Then we can find the equations of the circle with AB AC and BC as diameter. Then we can find the equations of any two radical axis and finally their point of intersection i.e radical centre. Further we can verify that this point is also the ortocentre of triangle ABC.