MathDB

Mid-points of the three sides X,Y and Z

Source: IMO LongList 1988, Hong Kong 6, Problem 30 of ILL

October 22, 2005

geometryvectorcircumcircleIMO Longlist

Problem Statement

In the triangle

ABC

let

D,E

and

F

be the mid-points of the three sides,

X,Y

and

Z

the feet of the three altitudes,

H

the orthocenter, and

P,Q

and

R

the mid-points of the line segment joining

H

to the three vertices. Show that the nine points

D,E,F,P,Q,R,X,Y,Z

lie on a circle.