Question

If the vertices of a triangle be (2, 1); (5, 2) and (3,4) then its circumcentre is

• A. $\left( \frac{13}{2},\frac{9}{2} \right)$
• B. $\left( \frac{13}{4},\frac{9}{4} \right)$
• C. $\left( \frac{9}{4},\frac{13}{4} \right)$
• D. None

Answer 1

Answer: (B)

$\left( \frac{13}{4},\frac{9}{4} \right)$

Answer 2

Let circumcentre be $O(x,y)$ and given points are

$A(2,1);B(5,2);C(3,4)$ and $OA^{2} = OB^{2} = OC^{2}$

∴$(x - 2)^{2} + (y - 1)^{2} = (x - 5)^{2} + (y - 2)^{2}$ .....(i)

and $(x - 2)^{2} + (y - 1)^{2} = (x - 3)^{2} + (y - 4)^{2}$ .....(ii)

On solving (i) and (ii), we get $x = \frac{13}{4},y = \frac{9}{4}$