MathDB

Simple geometry

Source: 2015 Flanders Mathematical Olympiad, Problem 2

April 27, 2015

geometry

Problem Statement

Consider two points

Y

and

X

in a plane and a variable point

P

which is not on

XY

. Let the parallel line to

YP

through

X

intersect the internal angle bisector of

\angle XYP

in

A

, and let the parallel line to

XP

through

Y

intersect the internal angle bisector of

\angle YXP

in

B

. Let

AB

intersect

XP

and

YP

in

S

and

T

respectively. Show that the product

|XS|*|YT|

does not depend on the position of

P

.

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