Question

In a triangle a point which is always equidistant from all the sides is,

• A. the point of intersection of internal angle bisectors
• B. the point of intersection of altitudes
• C. the point of intersection of medians
• D. none

Answer 1

Answer: (A)

the point of intersection of internal angle bisectors

The Incenter $\left(I\right)$ of a triangle is the point on the interior of the triangle that is equidistant from the three sides. Since a point interior to an angle that is equidistant from the two sides of the angle lies on the angle bisector, then $I$ must be on the angle bisector of each angle of the triangle.

So, In a triangle, a point which is always equidistant from all the sides is the point of intersection of internal angle bisectors.