Question

The distance between the orthocenter and circumcentre of the triangle with vertices (1, 2) (2, 1) and \(\Big(\frac{3+\sqrt{3}}{2},\frac{3+\sqrt{3}}{2}\Big)\) is

A. 0 

B. √2

C. 3 +√3

D. none of these

Answer 1

Let A(1, 2), B(2, 1) and C\(\Big(\Big(\frac{3+\sqrt{3}}{2}\Big),\Big(\frac{3+\sqrt{3}}{2}\Big)\Big)\)

 be the given points. 

Thus, ABC is an equilateral triangle. 

We know that the orthocentre and the circumcentre of an equilateral triangle are same. 

So, the distance between the orthocentre and the circumcentre of the trianglewith vertices (1, 2), (2, 1) and \(\Big(\Big(\frac{3+\sqrt{3}}{2}\Big),\Big(\frac{3+\sqrt{3}}{2}\Big)\Big)\) is 0