Question

how to find the circumcentre of a right angled triangle

Answer 1

Dear student,

For a right triangle, the circumcenter lies at the midpoint of the hypotenuse.

In a graphical solution,
1. Bisect the hypotenuse
2. Draw a line perpendicular to it where the bisector crosses the hypotenuse.
3. The point of intersection is the midpoint which is the Circumcenter. The radius is half the length of the hypotenuse.

In a mathematical solution,
The coordinates of the endpoints of the hypotenuse are given which are : (x1, y1) and (x2, y2)
Then the midpoint or the circumcenter, can be calculated as:

(X, Y) = ( (x1 + x2)/2, (y1 +y2)/2)

Regards