MathDB

Three lines

k, l, m

are drawn through a point

P

inside a triangle

ABC

such that

k

meets

AB

A_1

and

AC

A_2 \ne A_1

and

PA_1 = PA_2

l

meets

BC

B_1

and

BA

B_2 \ne B_1

and

PB_1 = PB_2

m

meets

CA

C_1

and

CB

C_2\ne C_1

and

PC_1=PC_2

. Prove that the lines

k,l,m

are uniquely determined by these conditions. Find point

P

for which the triangles

AA_1A_2, BB_1B_2, CC_1C_2

have the same area and show that this point is unique.

Problem Statement