3.4 Three equal segments - 1

Instruction: Given an angle ABC and a point M inside it, find points D on BA and E on BC and construct segments DM and ME such that BD = DM = ME.

Goal: 4L 6E

Available tools:

• Move
• Point
• Line
• Circle
• Perpendicular Bisector
• Perpendicular
• Angle Bisector
• Intersect

Pack: Gamma

Previous level: 3.3

Next level: 3.5

4L 6E solution

1. Construct the perpendicular bisector of BM, intersecting AB at D
2. Construct the circle with center M and radius DM, intersecting BC at E and F
3. Construct line DM
4. Construct line ME

2V solution

1. Construct line MF

Explanation

Point D is easy. Since it's equidistant to both B and M, then it must be on their perpendicular bisector.

Now that you know DM, since M is also equidistant to both D and E, then both D and E are on a circle with center M. You'll notice that there are two possibilities for E.