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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.

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    http://formulas.tutorvista.com/math/orthocenter-formula.html

    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.

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