MathDB

Initially, three non-collinear points,

A

B

, and

C

, are marked on the plane. You have a pencil and a double-edged ruler of width

1

. Using them, you may perform the following operations:
[*]Mark an arbitrary point in the plane. [*]Mark an arbitrary point on an already drawn line. [*]If two points

P_1

and

P_2

are marked, draw the line connecting

P_1

and

P_2

. [*]If two non-parallel lines

l_1

and

l_2

are drawn, mark the intersection of

l_1

and

l_2

. [*]If a line

l

is drawn, draw a line parallel to

l

that is at distance

1

away from

l

(note that two such lines may be drawn).
Prove that it is possible to mark the orthocenter of

ABC

using these operations.

Problem Statement