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Which of the following statements is true with respect to a triangle?
Question

Which of the following statements is true with respect to a triangle?

A.

The concurrent point of altitudes is called centroid.

B.

The sum of medians is less than perimeter.

C.

The concurrent point of internal angle bisectors is called orthocenter.

D.

Any two sides together are less than twice the median of remaining side.

Correct option is B

Concept Used:

Sum of medians of a triangle < perimeter of the triangle

Centroid is the point of concurrency of medians

Orthocenter is the point of concurrency of altitudes

In any triangle, the sum of any two sides is greater than the third side (Triangle Inequality)

Solution:
Option B is correct: "The sum of medians is less than perimeter."
This is a true and known property of triangles.

Other options are incorrect:

A: Altitudes meet at the orthocenter, not centroid.

C: Angle bisectors meet at the incenter, not orthocenter.

D: Incorrect triangle inequality relation.

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