10.2 Outer Tangent

Instruction: Construct an outer tangent between two circles.

Goal: 6L 8E 2V

Available Tools:

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

Pack: Kappa

Previous Level: 10.1

Next Level: 10.3

6L Solution

Let A and B be the centers of the circles.

1. Construct line AB, intersecting the two circles at C and D, with C and D between A and B.
2. Construct the perpendicular bisector of AB, intersecting AB at E.
3. Construct the perpendicular bisector of CD, intersecting AB at F.
4. Construct circle E with radius AE, intersecting bisector F at G.
5. Construct circle G with radius CG, intersecting circle A at H and circle B at I.
6. Construct line HI.

8E Solution

Let A and B be the centers of the circles.

1. Construct line AB, intersecting circle A at C and circle B at D, with C on the other side of A from B and D between A and B.
2. Construct circle C with radius AC, intersecting circle A at E.
3. Construct circle D with radius BD, intersecting circle B at F, with F being the point closer to E.
4. Construct line EF, intersecting AB at G.
5. Construct circle D with radius DG, intersecting AB at H.
6. Construct circle B with radius BG, intersecting AB at I.
7. Construct circle I with radius HI, intersecting the latest circle at J.
8. Construct line GJ.

2V Solution

From the 4L Solution

1. Let the other intersection between circle E and bisector F be J.
2. Construct circle J with radius CJ, intersecting circle A at K and circle B at L.
3. Construct line KL.