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Fuss lemma for parabolas

Source: III Caucasus Mathematical Olympiad

March 17, 2018

algebraquadratic trinomialconicsparabola

Problem Statement

Two graphs

G_1

and

G_2

of quadratic polynomials intersect at points

A

and

B

. Let

O

be the vertex of

G_1

. Lines

OA

and

OB

intersect

G_2

again at points

C

and

D

. Prove that

CD

is parallel to the

x

-axis.

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