Instruction: Construct a straight line through the given point that makes an angle of 60° with the given line.

Goal: 3L 4E

Available tools:

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

Pack: Delta

Previous level: 4.1

Next level: 4.3

3L solution

Let A be the given point.

1. Construct a circle with center A and an arbitrary radius, intersecting the line at B and C
2. Construct the circle with center B and radius AB, intersecting circle A at D and E
3. Construct the perpendicular bisector of CD

4E solution

Let A be the given point.

1. Construct a circle with center A and an arbitrary radius, intersecting the line at B and C
2. Construct the circle with center B and radius AB, intersecting circle A at D and E, and intersecting the line at F and G
3. Construct the circle with center F and radius DF, intersecting circle A at H
4. Construct line AH

Alternate 4E solution:

1. Construct a circle with center A and an arbitrary radius, intersecting the line at B and C
2. Construct the circle with center B and radius AB, intersecting circle A at D and E, and intersecting the line at F and G
3. Construct line DF, intersecting circle A at H
4. Construct line AH

2V solution

From the 3L solution:

1. Construct the perpendicular bisector of CE

From the 4E solution:

1. Construct the circle with center G and radius EG, intersecting circle A at I
2. Construct line AI

From the alternate 4E solution:

1. Construct line EG, intersecting circle A at I
2. Construct line AI