four special lines and four centres
In triangle ABC, D, E and F are mid points of the line segments. There are four special lines and four centers in any triangles. You may drag the points A, B, C and click the boxes to see the changes of the lines and centers.
1. What kinds of triangle ABC would be so that all special lines overlapped? 2. When would all centers lie on the same straight line? 3. Which centers must lie inside the triangle? 4. Which centers may lie outside the triangle? and when? 5. Which centers may on the edge of the triangle? and when? 6. Describe the relationship between the vertices of triangle ABC and the circumcentre. 7. Describe the relationship between the edges of triangle ABC and the incentre.