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Question: Which of the following always lies inside a triangle?
1. incenter
2. orthocenter
3. circumcenter
4. centroid


A ) 1 and 2
B ) 2 and 4
C ) 1 and 3
D ) 1 and 4

Steps to derive

1 Incenter is the point of concurrency of the interior angle bisectors of the triangle.

2 Centroid is the point of concurrency of the medians.

3 Essentially, these two lie inside the triangle.

4 Ortho center is the point of concurrency of the altitudes and circumcenter is the point of concurrency of the perpendicular bisectors.

5 These two points can be inside or outside the triangle depending on the type of triangle.

6 So, incenter and centroid are always inside the triangle.



Hence the right answer is Option D

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