Given points P, Q, R and S are the 4 special centres of triangle (Incentre, centroid, orthocentre, circumcentre). Can you identify which is which and explain why?
For any triangle, what is the minimum number of special centres inside the triangle? What are the centers? For what type of triangle this happens?
What is the condition for all 4 special centres to be collinear (lie on the same line)?
What is the condition for all 4 special centres to be coincide (meet at one point)?
Which special centres always collinear for any type of triangles?
What is ratio PQ:QS? Can you prove this ratio?