MathDB

Let

AA_1

be the bisector of a triangle

ABC

. Points

D

and

F

are chosen on the line

BC

such that

A_1

is the midpoint of the segment

DF

. A line

l

, different from

BC

, passes through

A_1

and intersects the lines

AB

and

AC

at points

B_1

and

C_1

, respectively. Find the locus of the points of intersection of the lines

B_1D

and

C_1F

for all possible positions of

l

.
(M. Karpuk)

Problem Statement