4

Part of 1995 APMO

Problems(1)

A moves around the circle

Source: APMO 1995

C

be a circle with radius

R

O

S

a fixed point in the interior of

C

AA'

BB'

be perpendicular chords through

S

. Consider the rectangles

SAMB

SBN'A'

SA'M'B'

SB'NA

. Find the set of all points

M

N'

M'

N

A

moves around the whole circle.

geometryrectanglecircumcircleparallelogramcyclic quadrilateralgeometry unsolved