How to solve the question using co-ordinate geometry? On the sides $BC,CA,AB$ of a given triangle are taken points $P,Q,R$ such that the triangle $PQR$ is of given species. Prove that the locus of the circumcentre of triangle $PQR$ is a straight line.
Here i am stuck at "species" of triangle. What does it actually mean, and how to approach it? Please help.

'of given species' means if triangle $ABC$ is equilateral then triangle $PQR$ would be equilateral too. If triangle$ABC$ is scalene, so would be triangle $PQR$, that too proportionally. i.e. triangle$ABC$ would be similar to triangle $PQR$. Now, you can find many such triangles inside the triangle $ABC$. And if you join the circumcenters of those triangles, you would get a straight line.
