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6.10 Symmetry of Four Lines
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 
5.11 Regular Hexagon
Instruction: Construct a regular hexagon with the given side. Goal: 7L 8E 
5.1 Parallel Line
Instruction: Construct a line parallel to the given line and through the given point. Goal: 2L 4E 
3.2 Triangle by Angle and Orthocenter
Instruction: Construct a segment connecting the sides of the angle to get a triangle whose orthocenter is in the point O. Goal: 3L 6E 
3.5 Circle through Point Tangent to Line
Instruction: Construct a circle through the point A that is tangent to the given line at the point B. Goal: 3L 6E 
8.1 Perimeter Bisector
Instruction: Construct a straight line through a vertex of the triangle that divides its perimeter in half. Goal: 4L 7E 3V 
8.2 Angle 54° Trisection
Instruction: Construct two rays that divide the given angle of 54° into three equal parts. Goal: 4L 5E 
7.7 Inscribed Circle
Instruction: Construct the incircle of the triangle. Goal: 4L 8E 
7.1 Sum of Areas of Squares
Instruction: Construct a square whose area equals the sum of the areas of the two given squares and all three have the common angle. Goal: 3L 6E 
4.8 Angle of 15°
Instruction: Construct an angle of 15° with the given side. Goal: 3L 5E 
6.6 Translate Segment
Instruction: Construct a segment from the given point parallel and equal to the given segment. Goal: 2L 6E 
6.8 Parallelogram
Instruction: Construct a parallelogram with the given side and the midpoint of the opposite side in the given point. Goal: 5L 8E 
5.8 Circumscribed Square
Instruction: Circumscribe a square about the circle. Two of its sides should be parallel to the given line. Goal: 6L 11E 
9.9 Triangle by Angle and Centroid
Instruction: Construct a segment connecting the sides of the angle to get a triangle whose centroid is in the point O. Goal: 5L 7E 
6.9 Nine Point Circle
Instruction: Construct a circle that passes through the midpoints of sides of the given acute triangle. Goal: 5L 9E 
4.4 Equilateral Triangle in Circle
Instruction: Inscribe an equilateral triangle in the circle using the given point as a vertex. The center of the circle is not given. Goal: 5L 6E 
5.2 Parallelogram by Three Vertices
Instruction: Construct a parallelogram whose three of four vertices are given. Goal: 4L 8E 
6.3 Copy Segment
Instruction: Construct a segment from the given point that is equal to the given segment annd lies on the same line with it. Goal: 3L 4E 
2.3 Angle of 30°
Instruction: Construct an angle of 30° with the given side. Goal: 3L 3E 
2.6 Drop a Perpendicular
Instruction: Drop a perpendicular from the point to the line. Goal: 2L 3E 
8.6 Torricelli Point
Instruction: Construct a point from which each side subtends an angle of 120 or 60. Goal: 4L 5E 2V 
5.9 Square in Square
Instruction: Inscribe a square in the square. A vertex is given. Goal: 6L 7E 
4.3 Circumscribed Equilateral Triangle
Instruction: Construct an equilateral triangle that is circumscribed about the circle and contains the given point. Goal: 5L 6E 
9.7 Minimum Perimeter  2
Instruction: Inscribe a triangle into the given one whose perimeter is the minimum possible. Goal: 6L 8E 
7.9 Segment by Midpoint
Instruction: Construct a segment with the ends on the sides of the angle such that the given point is its midpoint. Goal: 3L 5E
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