MathDB

Segment of constant length

Source: Arnoldo Aguilar, Central American Olympiad 2006, Problem 2

April 30, 2007

vectorgeometrygeometric transformationparallelogramtrapezoid

Problem Statement

Let

\Gamma

and

\Gamma'

be two congruent circles centered at

O

and

O'

, respectively, and let

A

be one of their two points of intersection.

B

is a point on

\Gamma

,

C

is the second point of intersection of

AB

and

\Gamma'

, and

D

is a point on

\Gamma'

such that

OBDO'

is a parallelogram. Show that the length of

CD

does not depend on the position of

B

.

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