MathDB

Parallelogram problem

Source: INMO 1997 Problem 1

October 6, 2005

geometryparallelogramtrigonometrycircumcirclegeometry solved

Problem Statement

Let

ABCD

be a parallelogram. Suppose a line passing through

C

and lying outside the parallelogram meets

AB

and

AD

produced at

E

and

F

respectively. Show that

AC^2 + CE \cdot CF = AB \cdot AE + AD \cdot AF .