Question

The circumcentre of an acute angled triangle is located inside the triangle . the circumcentre of an obtuse angled triangle is located outside the triangle .Where does the circumcentre of an right angled triangle lie ?
A) On the triangle
B) Outside the triangle
C) Inside the triangle
D) None of the above

Answer 1

Hint:
We are given about the circumcenter of the acute angle and obtuse angled triangles and now when we draw perpendicular bisectors of the sides of a right angled triangle we can see that they intersect at the hypotenuse with which we can come to an conclusion as circumcentre is the point of intersection of the perpendicular bisectors drawn from the vertices to the respective sides.

Complete step by step solution:
We are given that the circumcentre of an acute angled triangle is located inside the triangle
And the circumcentre of an obtuse angled triangled is located outside the triangle
Now circumcentre is the point of intersection of the perpendicular bisectors drawn from the vertices to the respective sides
And the circumcentre is equidistant from the vertices
So now when we draw perpendicular bisectors of the sides of an right angled triangle we can see that they intersect on the hypotenuse of the triangle

We can see that O is the circumcentre of the triangle ABC
Hence the circumcentre of the right angled triangle lies on the triangle

The correct option is A.

Note:
Additional information :
1) The centroid of a triangle is the intersection of the three medians of the triangle
2) The orthocenter of a triangle is the intersection of the triangle's three altitudes.