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 a right angled triangle lie?

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On the triangle

Outside the triangle

Inside the triangle

None of the above

answer is A.

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Detailed Solution

We are given that the circumcentre of an acute angled triangle is located inside the triangle
And the circumcentre of an obtuse angled triangle 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.

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