### ABC is a right-angled scalene triangle

In this case we have the hyperbola again. While it seems obvious that
the locus will pass through B the vertex at the right angle (obvious since
this will be the Orthocenter (H)) The question to be asked is can we predict
through wich of the remaining vertices will the hyperbola pass and which
one will it merely touch?

Claim: The hyperbola passes through the vertex at which the triangle has
the smallest angles while touching at the vertex at which the middle sized
angle.

To test the claim and watch a GSP sketch draw the locus click
here.

Back