posted by sivakumar
A right angled triangle has sides a and b where a<b. If the right angle is bisected then then find the distance between orthocentres of the smaller triangles using coordinate geometry.
This will give you the orthocenter, if you have the vertices of a triangle.
If you set up your right triangle with the right angle at C=(0,0) then let the other two vertices be at A=(a,0) and B=(0,b).
Then the right-angle bisector intersects the hypotenuse at D=(d,d) where d = ab/(a+b). (why?)
Now you have the vertices for your two smaller triangles. Find their orthocenters and then the distance between them.