Question

If the vertices of a triangle are $P(8,6),Q(8,-2)$ and $R(2,-2)$, then which of the following is/are correct?

• A. Coordinates of circumcentre of triangle PQR is $(5,2)$
• B. Coordinates of circumcentre of triangle PQR is $(2,5)$
• C. Circumradius of triangle PQR is $5$ units
• D. Circumradius of triangle PQR is $\sqrt{37}$ units

Answer 1

Answer: (A), (C)

The correct options are
A Coordinates of circumcentre of triangle PQR is $(5,2)$
C Circumradius of triangle PQR is $5$ units

Mid point of $PQ$ is $(8,2)$
Equation of perpendicular bisector of $PQ$ is
$y-2=-\left(\frac{8-8}{6+2}\right)(x-8)\Rightarrow y=2$
Mid point of $QR$ is $(5,-2)$
Equation of perpendicular bisector of $QR$ is
$y+2=-\left(\frac{8-2}{-2+2}\right)(x-5)\Rightarrow x=5$
So coordinates of circumcenter of $△PQR$ is $(5,2)$
and radius is $\sqrt{(8-5{)}^2+(6-2{)}^2}=5\text{units}$