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4SymmetricLinesDetailed.a724582e583349e456a02d6da70b909e.png

Instruction: Three lines are intersected in a point. Construct a line so that the set of all 4 lines is mirror symmetric.

Goal: 3L 4E

Available tools:

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

Pack: Zeta

Previous level: 6.9

Next level: 6.11

3L solution[]

Let O be the intersection of the three lines.

  1. Construct a circle with center O and an arbitrary radius, intersecting the lines at six points; let A, B and C be a set of three consecutive points
  2. Use the non-collapsing compass to construct the circle with radius AB and center C, intersecting circle O at D and E
  3. Construct line OD

4E solution[]

Given the triangle ABC.

  1. Construct a circle with center O and an arbitrary radius, intersecting the lines at six points; let A, B, C, D amd E be a set of five consecutive points
  2. Construct line AC, intersecting OB at F
  3. Construct the circle with center O and radius OF, intersecting AC at G
  4. Construct line OG

3V solution[]

From the 3L solution:

  1. Construct line OE
  2. Use the non-collapsing compass to construct the circle with radius BC and center A, intersecting circle O at F
  3. Construct line OF

From the 4E solution:

  1. Construct line BD, intersecting OC at H
  2. Construct the circle with center O and radius OH, intersecting BD at I
  3. Construct line OI
  4. Construct line CE, intersecting OD at J
  5. Construct the circle with center O and radius OJ, intersecting CE at K
  6. Construct line OK

Explanation[]

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