Question

Where is the circumcenter of this triangle located?

Answer 1

We know that the diagonals of a rectangle bisect each other.

So, If we draw the second diagonal of the rectangle, it will bisect the first diagonal, which is the hypotenuse of the triangle.

Also, in a rectangle, the bisectors of the sides and the diagonals are concurrent.

Hence, if we draw bisectors of the two sides of the given triangle, these bisectors and the second diagonal, which is the bisector of the hypotenuse, meet at a point.

Circumcenter of a triangle is nothing but the point of intersection of the bisectors of the sides of the triangle.

Since the above bisectors and the hypotenuse (the first diagonal of the rectangle) are concurrent, the circumcentre lies on the hypotenuse.

Hence, the circumcenter lies on the hypotenuse of the triangle.