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2014 JBMO Shortlist G2

Source: 2014 JBMO Shortlist G2

October 8, 2017

geometryJBMO

Problem Statement

Acute-angled triangle

{ABC}

with

{AB<AC<BC}

and let be

{c(O,R)}

it’s circumcircle. Diameters

{BD}

and

{CE}

are drawn. Circle

{c_1(A,AE)}

interescts

{AC}

at

{K}

. Circle

{{c}_{2}(A,AD)}

intersects

{BA}

at

{L}

.(

{A}

lies between

{B}

and

{L}

). Prove that lines

{EK}

and

{DL}

intersect at circle

c

.
by Evangelos Psychas (Greece)

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