9.9 Triangle by Angle and Centroid

Instruction: Construct a segment connecting the sides of the angle to get a triangle whose centroid is in the point O.

Goal: 5L 7E

Available Tools:

• Move
• Point
• Line
• Circle
• Perpendicular Bisector
• Perpendicular
• Angle Bisector
• Parallel
• Non-collapsing Compass
• Intersect

Pack: Iota

Previous Level: 9.8

Next Level: 9.10

5L Solution

Let O be the vertex of the angle and A the given point.

1. Construct the line parallel to one line through A, intersecting the other line at B.
2. Construct the line parallel to BO through A, intersecting the other line at C.
3. Construct circle A with radius AB, intersecting AB at D.
4. Construct circle A with radius AC, intersecting AC at E.
5. Construct line DE.

7E Solution

Let O be the vertex of the angle and A the given point.

1. Construct line AO.
2. Construct circle A with radius AO, intersecting AO at B.
3. Construct circle B with radius BA, intersecting AO at C and circle A at D and E.
4. Construct line DE, intersecting one line at F and AO at G.
5. Construct circle G with radius FG, intersecting DE at H.
6. Construct line CH, intersecting the other line at I.
7. Construct line GI.