Question

The distance between the orthocentre and the circumcentre of the triangle $PQR$ is?

• A. $\frac{25}{2}$
• B. $\frac{29}{2}$
• C. $\frac{37}{2}$
• D. $\frac{51}{2}$

Answer 1

The correct option is A $\frac{25}{2}$

Since the above triangle is a right angled triangle, right angled at $R(1,-7)$ the coordinates of the orthocentre will be the same as that of $R(1,-7)$
The circumcentre $\left(C\right)$ will be the mid point of $PQ$
that is $(\frac{-23}{2},-7)$
Thus $CR$
$=\sqrt{(\frac{23}{2}+1{)}^2}$
$=\frac{25}{2}$