MathDB

2016 Guts #20

Source:

December 24, 2016

Problem Statement

Let

ABC

be a triangle with

AB=13

,

AC=14

, and

BC=15

. Let

G

be the point on

AC

such that the reflection of

BG

over the angle bisector of

\angle B

passes through the midpoint of

AC

. Let

Y

be the midpoint of

GC

and

X

be a point on segment

AG

such that

\frac{AX}{XG}=3

. Construct

F

and

H

on

AB

and

BC

, respectively, such that

FX \parallel BG \parallel HY

. If

AH

and

CF

concur at

Z

and

W

is on

AC

such that

WZ \parallel BG

, find

WZ

.

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