Erect a Perpendicular

Instruction: Erect a perpendicular from the point on the line.

Available tools:

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

Previous puzzle: 2.6

Next puzzle: 2.8

1L solution

Let O be the point.

1. Construct the angle bisector of ∠AOB, with A and B two arbitrary points on the line on two opposite sides from point O

3E solution

Let O be the point.

1. Construct a circle with an arbitrary center A not on the line and radius OA, intersecting the line at B
2. Construct line AB, intersecting circle A at C
3. Construct line OC

Explanation

Solution 1L is simple as a line is an angle of 180°, so its angle bisector will divide it into two angles of 90° and will therefore be perpendicular to it. Just have the vertex of the 180° angle be point O.

Solution 3E makes use of Thales's theorem. You are constructing the inscribed triangle OBC with its side BC a diameter of the circle, which makes OBC a right triangle with ∠BOC=90°.