MathDB

2018 Team #4

Source:

February 12, 2018

Problem Statement

In acute triangle

ABC

, let

D

,

E

, and

CA

be the feet of the altitudes from

A

,

B

, and

C

respectively, and let

L

,

M

, and

N

be the midpoints of

BC

,

CA

and

AB

, respectively. Lines

DE

and

NL

intersect at

X

, lines

DF

and

LM

intersect at

Y

, and lines

XY

and

BC

intersect at

Z

. Find

\frac{ZB}{ZC}

in terms of

AB

,

AC

, and

BC

.

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