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Triangles: Incenter, Centroid, Orthocenter, Circumcenter

This aptitude practice question is a geometry question and tests your understanding of the definition of 4 important lines that can be drawn in a triangle and the points where those lines meet. This one is a Easy question.

Question

Which of the following is incorrect?

  1. An incentre is a point where the angle bisectors meet.
  2. The median of any side of a triangle bisects the side at right angle.
  3. The point at which the three altitudes of a triangle meet is the orthocentre
  4. The point at which the three perpendicular bisectors meet is the centre of the circumcircle.

  Correct Answer      Choice (2). The median of any side of a triangle bisects the side at right angle.


Explanatory Answer

Choice (1) The point at which the three angle bisectors meet is the incentre and it is the centre of incircle that is drawn to any triangle. Choice (1) is true and is not the answer.

Choice (2) The median of any triangle will bisect a side, but it need not necessarily bisect the side at right angles. All 3 medians of an equilateral triangle and the median to the side that is not equal in an isosceles triangle meet the side at right angles. So, stating that median of any triangle will bisect the side at right angles is incorrect.

Therefore, choice (2) is the answer.

Choice (3) The 3 altitudes of a triangle meet concurrently at a point and the point is known as orthocentre. Choice (3) is true and is not the answer.

Choice (4) The 3 perpendicular bisectors of a triangle meet concurrently at a point and the point is known as circumcentre. Choice (4) is true and is not the answer

  The correct answer is Choice (2).

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