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CircleTangentLLLDetailed.4179e94a590225817da8915237fa26bc.png

Instruction: Construct a circle that is tangent to the three given lines. Two of the lines are parallel.

Goal: 4L 6E

Available tools:

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

Pack: Eta

Previous level: 7.7

Next level: 7.9

4L solution[]

Given the intersections of the lines A and B.

  1. Construct the angle bisector of ∠CAB, with C an arbitrary point on one of the parallel lines.
  2. Construct the angle bisector of ∠ABD, with D an arbitrary point on the other parallel line and on the same side as C from the third given line, intersecting the angle bisector of ∠CAB at E
  3. Construct the perpendicular to AB through E, intersecting AB at F
  4. Construct the circle with center E and radius EF

6E solution[]

Given the intersections of the lines A and B.

  1. Construct the circle with center A and radius AB, intersecting the parallel line through A at C and D
  2. Construct line BC
  3. Construct the circle with center C and radius BC
  4. Construct the circle with center D and radius CD, intersecting circle C at E and F
  5. Construct line EF, intersecting BC at G and AC and H
  6. Construct the circle with center G and radius GH

2V solution[]

From the 4L solution:

  1. Construct the angle bisector of ∠GAB, with G an arbitrary point on AC and on the other side of C from A.
  2. Construct the angle bisector of ∠ABH, with H an arbitrary point on BD and on the other side of D from B, intersecting the angle bisector of ∠GAB at I
  3. Construct the perpendicular to AB through I, intersecting AB at J
  4. Construct the circle with center I and radius IJ

Explanation[]

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