3

Part of 2016 Finnish National High School Mathematics Comp

Problems(1)

length of segment of projections independent of altitude selected

Source: Finland 2016, p3

From the foot of one altitude of the acute triangle, perpendiculars are drawn on the other two sides, that meet the other sides at

P

Q

. Show that the length of

PQ

does not depend on which of the three altitudes is selected.

altitudelengthgeometry