MathDB

A moves around the circle

Source: APMO 1995

March 11, 2006

geometryrectanglecircumcircleparallelogramcyclic quadrilateralgeometry unsolved

Problem Statement

Let

C

be a circle with radius

R

and centre

O

, and

S

a fixed point in the interior of

C

. Let

AA'

and

BB'

be perpendicular chords through

S

. Consider the rectangles

SAMB

,

SBN'A'

,

SA'M'B'

, and

SB'NA

. Find the set of all points

M

,

N'

,

M'

, and

N

when

A

moves around the whole circle.

Back to Problems View on AoPS