Find the circumcentre of a triangle whose vertex are $(0,0),(4,0)$ and $(0,6)$

Let A (0,0) B (4,0) and C (0,6)

AB has a constant ordinate and

hence t is on x axis (ordinate=0)

AC has a constant abscissa (=0)

Hence it is on y axis

$\Rightarrow AB\perp AC$

Hence the given triangle is a

right angled triangle ,at $\angle A$

so, BC is the hypotenuse,

and circumferential is the midpoint

of the hypotenuse.

Hence . midpoint of BC

$(\frac{4+0}{2},\frac{0+6}{2})$

$(\frac{4}{2},\frac{6}{2})=(2,3)$

$\therefore$ The circumcentre is (2,3)