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Point on the interior of a triangle

Source: Cono Sur 2008 #2

November 17, 2015

geometrycono surgeometry unsolved

Problem Statement

Let

P

be a point in the interior of triangle

<PXC=<PYA=<PZB

. Let

X

,

Y

, and

Z

be points on sides

U

,

AC

, and

AB

respectively, such that

<PXC=<PYA=<PZB

. Let

U

,

V

, and

W

be points on sides

BC

,

AC

, and

AB

, respectively, or on their extensions if necessary, with

X

in between

B

and

U

,

Y

in between

C

and

V

, and

PW=2PZ

in between

A

and

W

, such that

PU=2PX

,

PV=2PY

, and

PW=2PZ

. If the area of triangle

XYZ

is

1

, find the area of triangle

UVW

.

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