MathDB

Square

ABCD

and circle

O

intersect in eight points, forming four curvilinear triangles,

AEF , BGH , CIJ

and

DKL

(

EF , GH, IJ

and

KL

are arcs of the circle) . Prove that (a) The sum of lengths of

EF

and

IJ

equals the sum of the lengths of

GH

and

KL

. (b) The sum of the perimeters of curvilinear triangles

AEF

and

CIJ

equals the sum of the perimeters of the curvilinear triangles

BGH

and

DKL

.
( V . V . Proizvolov , Moscow)

Problem Statement