Points the same distance from two lines that meet at 120°

Step by step

The question

Question: draw the locus of the points that are the same distance from two lines that meet at 120°.

A locus is the set of all the points that follow a rule.

Here: the same distance from both lines.

1 Draw the angle

Draw the two lines meeting at V, with 120° between them.

2 Arc from the corner

From the corner V, draw an arc that cuts both lines, at P and Q.

3 Arcs from P and Q

With the same opening from P and from Q, draw two arcs.

They cross at R.

Careful!

Keep the compass the same for both arcs.

Then R is the same distance from both lines.

4 Join V and R

Join V to R with a ruler, and go on.

This line cuts the angle in half: 60° and 60°.

5 Check

Let's check with a protractor: both halves are 60°.

So it is right!

Let's look back.

First: draw the angle.

Then: arc from the corner.

Then: arcs from P and Q.

Then: join V and R.

Last: check.