The distance between the orthocentre and circumcentre of the triangle with vertices `(1,2),\ (2,1)\ a n d\ ((3+sqrt(3))/2,(3+sqrt(3))/2)` is
a. 0 b. `sqrt(2)` c. `3+sqrt(3)` d. none of these

Explanation

To find the distance between the orthocenter and circumcenter of the triangle with vertices \( A(1, 2) \), \( B(2, 1) \), and \( C\left(\frac{3+\sqrt{3}}{2}, \frac{3+\sqrt{3}}{2}\right) \), we will follow these steps:

### Step 1: Calculate the lengths of the sides of the triangle
We will use the distance formula to find the lengths of the sides \( AB \), \( BC \), and \( AC \).

#### Length of \( AB \):
Using the distance formula:
\[
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