MathDB

Let

ABC

be an acute-angled triangle,

C'

and

A'

be arbitrary points on the sides

AB

and

BC

respectively, and

B'

be the midpoint of the side

AC

.
(a) Prove that the area of triangle

A'B'C'

is at most half the area of triangle

ABC

.
(b) Prove that the area of triangle

A'B'C'

is equal to one fourth of the area of triangle

ABC

if and only if at least one of the points

A'

C'

is the midpoint of the corresponding side.
(E Cherepanov)

Problem Statement