SOLUTION: Q: Let the vertices of triangle be (0, 0), (3, 0) and (0, 4). Find its: (i) Orthocenter (ii) Radius of the inscribed circle

You can make a sketch, or, like me, simply look attentively at coordinates of the vertices.


Then you will notice that the triangle is a RIGHT-ANGLED triangle with the right angle vertex 
at the origin of the coordinate system.


THEREFORE, the othocenter (the intersection point of altitudes) is the origin point (0,0).



Next, in a right angled triangle, the radius of incribed circle is


    r = ,


where P and B are the legs and H is the hypotenuse.


In your case,  P = 3,  B = 4, H = 5, THEREFORE, the radius of the inscribed circle is


    r =  =  = 1 unit.