Acute triangle with perpendicular lines
Source: RMO, Grade 7, Problem 1
April 30, 2008
trigonometrygeometrycircumcirclegeometric transformation
Problem Statement
Let be an acute angled triangle with . Let be the foot of the altitude from on , and let be the foot of the perpendicular from on . Let be a point on the segment . Show that the lines and are perpendicular if and only if EF\cdot DC \equal{} BD \cdot DE.