Question

The inradius of an equilateral triangle whose one side length is 2, is ..?

Answer 1

The median, altitude, perpendicular bisector and angle-bisector of an equilateral triangle are all coincident. So the in-radius is one-third of the median AD shown below.
Can you figure out the distance OD knowing that OD = (1/3)AD, since the centroid is at 1/3 of the median.

Answer 2

Ooh, I got the correct answer. Thank you so much!! I wanna ask one thing, is in-radius formula always 1/3 of the height/altitude of the triangle?

Answer 3

Noooo, only for equilateral triangles.
For a general triangle, the in-radius is obtained by the intersection of the angle bisectors.
Thank you for reminding me to indicate the general method.
:)