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Square2VDetailed.png

Instruction: Given two vertices of a square. Construct the two other vertices using only a compass.

Goal: 7L 7E Available tools:

  • Move
  • Point
  • Circle
  • Intersect

Pack: Delta

Previous level: 4.10

Next level: 5.1

7L 7E solution[]

Euclidea 4.11 solutions diagram.png

Let A and B be the given vertices.

  1. Construct the circle with center A and radius AB
  2. Construct the circle with center B and radius AB, intersecting circle A at C and D
  3. Construct the circle with center C and radius CD, intersecting circle A at E and circle B at F
  4. Construct the circle with center E and radius BE
  5. Construct the circle with center F and radius AF, intersecting circle E at G and H
  6. Construct the circle with center A and radius AG, intersecting circle B at I and J, with I on the same side as G from AB
  7. Construct the circle with center B and radius BG, intersecting circle A radius AB at K and L, with K on the same side as I from AB
  8. Point at I
  9. Point at K

3V solution[]

  1. Point at J
  2. Point at L
  3. Construct the circle with center G and radius GI, intersecting circle A at M and circle B at N
  4. Construct the circle with center K and radius KM
  5. Construct the circle with center I and radius IN, intersecting circle K at O
  6. Construct the circle with center A and radius AO
  7. Construct the circle with center B and radius BO, intersecting circle A radius AO at P
  8. Point at P

Explanation[]

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