MathDB

2009 JBMO Shortlist G1

Source: 2009 JBMO Shortlist G1

October 8, 2017

geometryJBMO

Problem Statement

Parallelogram

{ABCD}

is given with

{AC>BD}

, and

{O}

intersection point of

{AC}

and

{BD}

. Circle with center at

{O}

and radius

{OA}

intersects extensions of

{AD}

and

{AB}

at points

{G}

and

{L}

, respectively. Let

{Z}

be intersection point of lines

{BD}

and

{GL}

. Prove that

\angle ZCA={{90}^{{}^\circ }}

.

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