Geometry Geometry

Question

Your sister claims that the heights of any traingle intersect in a point that is the center of both inscribed and circumscribed circle of that traingle. Your brother thinks such traingle does not exist. Correct their statements and explain them the mistakes they made.

Answer 1

The altitudes are concurrent but not at either the incenter nor the circumcenter.

The incenter is the intersection of the angle bisectors.

The circumcenter is the intersection of the perpendicular bisectors of the sides.

What do you know about an equilateral triangle?

P.S.

I have trouble typing "triangle" correctly too...but you need to proofread!