Euclidea Wiki

Instruction: Let |AB|=1. Construct a point C on the ray AB such that the length of AC is equal to √3.

Goal: 3L 3E

Available tools:

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

Pack: Delta

Previous level: 4.6

Next level: 4.8

3L 3E solution[]

  1. Construct the circle with center B and radius AB, intersecting the ray at D
  2. Construct the circle with center D and radius BD, intersecting circle B at E
  3. Construct the circle with center A and radius AE, intersecting the ray at C
  4. Point at C
    4.7-3L 3E.png


  • AB = 1 = BD, DE = 1
  • AD = 2
  • AED = 90o based on Thales Theorem

Using the 30-60-90 special triangle, we can deduce that side AE = . AE and AC are both radii of the circle centered at A.