Euclidea Wiki

Instruction: Construct a point on the given ray to get a segment with length equal to the harmonic mean of the two adjacent segments.

Goal: 4L 4E

Available Tools:

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

Pack: Iota

Previous Level: 9.7

Next Level: 9.9

4L 4E Solution[]

Given line AB, let C be the intersection of AB and the other line.

  1. Construct circle C with radius AC, intersecting line C at D and AB at E.
  2. Construct circle D with radius DE.
  3. Construct line DE, intersecting circle D at F.
  4. Construct line BF, intersecting CD at G.
  5. Point at G.