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2016 Latvia National Olympiad 3rd Round Grade12Problem2

Source:

July 22, 2016

geometryincenter

Problem Statement

Triangle

ABC

has incircle

\omega

and incenter

I

. On its sides

AB

and

BC

we pick points

P

and

Q

respectively, so that

PI = QI

and

PB > QB

. Line segment

QI

intersects

\omega

in

T

. Draw a tangent line to

\omega

passing through

T

; it intersects the sides

AB

and

BC

in

U

and

V

respectively. Prove that

PU = UV + VQ

!

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