(467) 1

Part of 1995 Tournament Of Towns

Problems(1)

TOT 467 1995 Autumn J A1 - point equidistant from sides of triangle

Source:

Prove that inside any acute-angled triangle, there exists a point

P

such that the feet of the perpendiculars dropped from

P

to the sides of the triangle are the vertices of an equilateral triangle.
(NB Vassiliev)