MathDB

Suppose

S

is a convex figure in plane with area

10

. Consider a chord of length

3

S

and let

A

and

B

be two points on this chord which divide it into three equal parts. For a variable point

X

S-\{A,B\}

, let

A'

and

B'

be the intersection points of rays

AX

and

BX

with the boundary of

S

. Let

S'

be those points

X

for which

AA'>\frac{1}{3} BB'

. Prove that the area of

S'

is at least

6

.
Proposed by Ali Khezeli

Problem Statement