If in triangle ABC, A = (1, 10), circumcentre =  and orthocenter =  then the co-ordinates of mid-point of side opposite to A is :

To find the coordinates of the mid-point of the side opposite to vertex A in triangle ABC, we will need to understand the relationship between the vertices, circumcenter, and orthocenter. Let's denote the vertex coordinates and use the properties of the triangle.

Step 1: Break Down the Problem

1. Identify the coordinates of point A (given as $A = (1, 10)$).
2. We know the circumcenter and orthocenter must relate to points B and C.
3. Find the mid-point of side BC, which is opposite to A.

Step 2: Relevant Concepts

• The mid-point $M$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Step 3: Analysis and Detail

Since we don't have the coordinates of points B and C explicitly, we cannot calculate the coordinates of the mid-point without additional information.

Step 4: Verify and Summarize

To provide a definitive answer for the mid-point of side BC, we need the coordinates of points B and C. This information must be computed based on the circumcenter and orthocenter values, which are missing in the problem statement.

Final Answer

Without the coordinates of points B and C or additional details about the circumcenter and orthocenter, we cannot determine the mid-point of side BC. Please provide the coordinates of B and C or the circumcenter and orthocenter to proceed further.