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10.3.jpg

Instruction: Construct an inner 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: 10.2

Next Level: 10.4

6L 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 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 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 further from 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.

Explanation[]

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