MathDB

Let

a_1,b_1,c_1

are three lines each two of them are mutually crossed and aren't parallel to some plane. The lines

a_2,b_2,c_2

intersect the lines

a_1,b_1,c_1

at the points

a_2

A

C_2

B_1

;

b_2

C_1

B

A_2

;

c_2

B_2

A_1

C

respectively in such a way that

A

is the perpendicular bisector of

B_1C_2

B

is the perpendicular bisector of

C_1A_2

and

C

is the perpendicular bisector of

A_1B_2

. Prove that:
(a)

A

is the perpendicular bisector of

B_2C_1

B

is the perpendicular bisector of

C_2A_1

and

C

is the perpendicular bisector of

A_2B_1

; (b) triangles

A_1B_1C_1

and

A_2B_2C_2

are the same.

Problem Statement