Question

Paul draws triangle ABC and the medians from vertices A and B. He finds that the medians intersect at a point and he labels this point X.Paul claims that point X lies outside triangle ABC . Do you think this is possible? Complete the explanation .

Answer 1

We can conclude from this that the triangle ABC is obtuse angled triangle.

Explanation:

Paul draws triangle ABC and the medians from vertices A and B.

He finds that the median intersects at a point and he labels this point X.

Now, Paul claims that point X (i.e. the centroid of the triangle) lies outside the triangle ABC.

Therefore, we can conclude from this that the triangle ABC is an obtuse-angled triangle.

Because, in case of an acute-angled triangle the centroid will be inside the circle, in case of a right triangle the centroid will be on the hypotenuse and in case of an obtuse-angled triangle the centroid will be outside the triangle. (Answer)