How can we construct C between A and B s.t. AB = α AC with compass-straightedge method?

Question

How can we construct $C$ between $A$ and $B$ such that $\vec{AB}=\alpha \vec{AC}$ where

$\alpha=\sqrt{3/2}$ and
$\alpha=\pi$?

The constraints is that we have to use the strict version of the geometrical construction with compass-straightedge method. The compass will collapse whenever it leaves the drawing plane.

I totally have no idea as the number $\alpha$ is difficult to produce, especially the second case.

This is equivalent to constructing a line of length $\alpha^{-1}$ — AlexR, Nov 08 '13 at 16:14
@HagenvonEitzen: How about the circumference of a semi-circle? Can we take advantage of it? — kiss my armpit, Nov 08 '13 at 16:18

score 3 · Answer 1 · answered Nov 22 '13 at 23:17

3

Maybe the following figure can help you draw the first case.

enter image description here

answered Nov 22 '13 at 23:17

RicardoCruz

3,693

How can we construct C between A and B s.t. AB = α AC with compass-straightedge method?

1 Answers1