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2015 JBMO Shortlist G5

Source: 2015 JBMO Shortlist G5

October 8, 2017

geometryJBMOsimilar trianglesincircle

Problem Statement

Let

ABC

be an acute triangle with

{AB\neq AC}

. The incircle

{\omega}

of the triangle touches the sides

{BC, CA}

and

{AB}

at

{D, E}

and

{F}

, respectively. The perpendicular line erected at

{C}

onto

{BC}

meets

{EF}

at

{M}

, and similarly the perpendicular line erected at

{B}

onto

{BC}

meets

{EF}

at

{N}

. The line

{DM}

meets

{\omega}

again in

{P}

, and the line

{DN}

meets

{\omega}

again at

{Q}

. Prove that

{DP=DQ}

.
Ruben Dario & Leo Giugiuc (Romania)

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