Question

Draw an equilateral triangle. Draw its altitudes, medians and angle bisectors. Explain your observation.

Answer 1

Draw an equilateral triangle ABC.
Draw medians AD, BE and CF to BC, AC and AB, respectively.
We observe that AD, BE and CF are the altitudes and angle bisectors also.
They all meet at one point, namely M, inside the triangle, which is the orthocentre, centroid and incentre.