MathDB

we have a triangle

ABC

and make rectangles

ABA_1B_2

BCB_1C_2

and

CAC_1A_2

out of it.
then pass a line through

A_2

perpendicular to

C_1A_2

and pass another line through

A_1

perpendicular to

A_1B_2

.
let

A'

the common point of this two lines. like this we make

B'

and

C'

.
prove

AA'

BB'

and

CC'

intersect each other in a same point.

Problem Statement