3

Part of 1978 Kurschak Competition

Problems(1)

H >=r+R where H is max altitude

Source: 1978 Hungary - Kürschák Competition p3

A triangle has inradius

r

and circumradius

R

. Its longest altitude has length

H

. Show that if the triangle does not have an obtuse angle, then

H \ge r+R

. When does equality hold?

geometryGeometric Inequalitiesinequalities