MathDB

constancy of side product as point varies along line

Source: Croatia 2000 3rd Grade P1

May 9, 2021

geometry

Problem Statement

Let

B

and

C

be fixed points, and let

A

be a variable point such that

\angle BAC

is fixed. The midpoints of

AB

and

AC

are

D

and

E

respectively, and

F,G

are points such that

DF\perp AB

EG\perp AC

and

BF

and

CG

are perpendicular to

BC

. Prove that

BF\cdot CG

remains constant as

A

varies.