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AEqualSegments1Detailed.e371b2279a1a4d2febc1ad105ca95582.png

Instruction: Given an angle ABC and a point M inside it, find points D on BA and E on BC and construct segments DM and ME such that BD = DM = ME.

Goal: 4L 6E

Available tools:

  • Move
  • Point
  • Line
  • Circle
  • Perpendicular Bisector
  • Perpendicular
  • Angle Bisector
  • Intersect

Pack: Gamma

Previous level: 3.3

Next level: 3.5

4L 6E solution[]

  1. Construct the perpendicular bisector of BM, intersecting AB at D
  2. Construct the circle with center M and radius DM, intersecting BC at E and F
  3. Construct line DM
  4. Construct line ME

2V solution[]

  1. Construct line MF

Explanation[]

Point D is easy. Since it's equidistant to both B and M, then it must be on their perpendicular bisector.

Now that you know DM, since M is also equidistant to both D and E, then both D and E are on a circle with center M. You'll notice that there are two possibilities for E.

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