In the triangle
let the feet of the altitudes be
. The circle with diameter
at two points other than
to form a segment of length
; similarly define
. Prove that
The segments of equal length are drawn in blue.
 D. Djukić, V. Janković, I. Matić, and N. Petrović, The IMO Compendium
, 2nd ed., New York: Springer, 2011 p. 73.