Solver and explanations: on Github.

Euclidea 1.1: Angle of 60°

A B C

* A: given (-100.00,0.00)
* B: given (100.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (0.00,173.21)
line: (AC)

Euclidea 1.2: Perpendicular Bisector

A B C D

* A: given (-100.00,0.00)
* B: given (100.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (0.00,-173.21)
* D = ⊙AB x ⊙BA (0.00,173.21)
line: (CD)

Euclidea 1.3: Midpoint

A B C D E

* A: given (-100.00,-20.00)
* B: given (100.00,20.00)
line: (AB)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (34.64,-173.21)
* D = ⊙AB x ⊙BA (-34.64,173.21)
line: (CD)
* E = (AB) x (CD) (0.00,0.00)

Euclidea 1.4: Circle in Square

A B C D E F H G

* A: given (-80.00,80.00)
* B: given (80.00,80.00)
circle: ⊙AB
circle: ⊙BA
* C: given (80.00,-80.00)
line: (AC)
* E = ⊙AB x ⊙BA (0.00,-58.56)
* F = ⊙AB x ⊙BA (0.00,218.56)
line: (EF)
* G = (AC) x (EF) (0.00,-0.00)
* H = (AB) x (EF) (0.00,80.00)
circle: ⊙GH

Euclidea 1.5: Rhombus in Rectangle

B C D A E G F

* B: given (81.12,33.99)
* C: given (81.12,-33.99)
circle: ⊙BC
* A: given (-81.12,33.99)
circle: ⊙BA
* E = (BC) x ⊙BC (81.12,101.96)
line: (AE)
* F = ⊙BA x (AE) (194.92,149.64)
line: (BF)
* D: given (-81.12,-33.99)
* G = ⊙BC x (AE) (32.67,81.66)
line: (DG)

Euclidea 1.6: Circle Center

B C D F G E H

* B: given (135.81,63.68)
* C: given (142.58,-46.60)
circle: ⊙BC
circle: ⊙CB
* D = ⊙AB x ⊙BC (55.36,139.41)
circle: ⊙DB
* E = ⊙CB x ⊙DB (62.13,29.13)
line: (BE)
* F = ⊙BC x ⊙CB (43.69,2.68)
* G = ⊙BC x ⊙CB (234.70,14.40)
line: (FG)
* H = (BE) x (FG) (0.00,0.00)

Euclidea 1.7: Inscribed Square

A B C D E F H G I

* B: given (0.00,150.00)
* A: given (0.00,0.00)
circle: ⊙BA
* C = ⊙AB x ⊙BA (129.90,75.00)
line: (AC)
* D = ⊙AB x ⊙BA (-129.90,75.00)
circle: ⊙CD
* E = ⊙AB x ⊙CD (0.00,-150.00)
* F = (AC) x ⊙CD (354.90,204.90)
line: (EF)
* G = ⊙AB x (EF) (150.00,0.00)
line: (BG)
* H = (AC) x ⊙CD (-95.10,-54.90)
line: (EH)
* I = ⊙AB x (EH) (-150.00,0.00)
line: (BI)

Euclidea 2.1: Angle Bissector

A B D E

* A: given (0.00,0.00)
* B: given (150.00,0.00)
circle: ⊙AB
circle: ⊙BA
* D = (AC) x ⊙AB (102.07,109.92)
circle: ⊙DA
* E = ⊙BA x ⊙DA (252.07,109.92)
line: (AE)

Euclidea 2.2: Intersection of Angle Bisectors

A B C D F E G H

* A: given (-120.00,-25.40)
* B: given (-5.54,123.00)
circle: ⊙AB
circle: ⊙BA
* D = (AC) x ⊙AB (67.34,-30.72)
circle: ⊙DA
* E = ⊙BA x ⊙DA (181.80,117.68)
line: (AE)
* F = (BC) x ⊙BA (145.92,12.62)
circle: ⊙FB
* G = ⊙AB x ⊙FB (31.46,-135.78)
line: (BG)
* H = (AE) x (BG) (7.07,34.84)

Euclidea 2.3: Angle of 30°

A B C D

* B: given (0.00,0.00)
* A: given (-150.00,0.00)
circle: ⊙BA
* C = (AB) x ⊙BA (150.00,0.00)
circle: ⊙CB
* D = ⊙BA x ⊙CB (75.00,129.90)
line: (AD)

Euclidea 2.4: Double Angle

A B D E

* A: given (-150.00,0.00)
* B: given (0.00,0.00)
circle: ⊙AB
* D = (AC) x ⊙AB (-16.89,69.15)
circle: ⊙DB
* E = ⊙AB x ⊙DB (-63.75,122.72)
line: (AE)

Euclidea 2.5: Cut Rectangle

E B C D A F

* B: given (81.12,33.99)
* D: given (-81.12,-33.99)
line: (BD)
* C: given (81.12,-33.99)
* A: given (-81.12,33.99)
line: (CA)
* E: given (152.10,146.78)
* F = (BD) x (CA) (-0.00,0.00)
line: (EF)

Euclidea 2.6: Drop a Perpendicular

A B C D

* A: given (-100.00,0.00)
* C: given (0.00,79.00)
circle: ⊙AC
* B: given (-275.10,0.00)
circle: ⊙BC
* D = ⊙AC x ⊙BC (0.00,-79.00)
line: (CD)

Euclidea 2.7: Erect a Perpendicular

A B C D E

* C: given (78.00,84.00)
* B: given (0.00,0.00)
circle: ⊙CB
* D = (AB) x ⊙CB (156.00,0.00)
line: (CD)
* E = ⊙CB x (CD) (0.00,168.00)
line: (BE)

Euclidea 2.8: Tangent to Circle at Point

A B C D E

* C: given (144.61,39.83)
* B: given (83.88,124.36)
circle: ⊙CB
* D = ⊙AB x ⊙CB (135.72,-63.87)
circle: ⊙BD
* E = ⊙CB x ⊙BD (245.73,15.18)
line: (BE)

Euclidea 2.9: Circle Tangent to Line

C A D E F

* A: given (112.00,0.00)
* C: given (0.00,125.00)
circle: ⊙AC
* D = (AB) x ⊙AC (-55.84,0.00)
circle: ⊙DC
* E = ⊙AC x ⊙DC (0.00,-125.00)
line: (CE)
* F = (AB) x (CE) (0.00,0.00)
circle: ⊙CF

Euclidea 2.10: Сircle in Rhombus

A B C D E F G H

* A: given (150.00,0.00)
* C: given (-150.00,0.00)
line: (AC)
* B: given (0.00,-122.20)
* D: given (0.00,122.20)
line: (BD)
* E = (AC) x (BD) (-0.00,0.00)
circle: ⊙AE
* F = (AB) x ⊙AE (266.29,94.74)
* G = (DA) x ⊙AE (33.71,94.74)
line: (FG)
* H = (BD) x (FG) (0.00,94.74)
circle: ⊙EH

Euclidea 3.1: Chord Midpoint

A C B D E

* A: given (0.00,0.00)
* C: given (0.00,54.11)
line: (AC)
* B: given (111.00,126.90)
circle: ⊙BC
* D = (AC) x ⊙BC (-0.00,199.69)
line: (BD)
* E = ⊙BC x (BD) (222.00,54.11)
line: (CE)

Euclidea 3.2: Triangle by Angle and Orthocenter

A B C D E G F H

* A: given (-120.23,10.00)
* D: given (87.00,56.00)
circle: ⊙AD
* B: given (145.00,0.00)
circle: ⊙BD
* E = ⊙AD x ⊙BD (82.95,-51.47)
line: (DE)
* C: given (109.70,176.30)
circle: ⊙CD
* F = ⊙AD x ⊙CD (-11.66,192.41)
line: (DF)
* G = (AC) x (DE) (91.03,162.79)
* H = (AB) x (DF) (127.01,0.68)
line: (GH)

Euclidea 3.3: Intersection of Perpendicular Bisectors

A B C D E F

* D: given (87.00,56.00)
* A: given (-100.00,-12.30)
circle: ⊙DA
* E = (AB) x ⊙DA (279.35,4.67)
* F = (AC) x ⊙DA (167.69,238.00)
line: (EF)

Euclidea 3.4: Three equal segments - 1

A B C D E F G H

* A: given (-100.00,31.30)
* D: given (97.00,65.00)
circle: ⊙AD
circle: ⊙DA
* E = ⊙AD x ⊙DA (27.69,-122.46)
* F = ⊙AD x ⊙DA (-30.69,218.76)
line: (EF)
* G = (AC) x (EF) (-7.92,85.67)
line: (DG)
circle: ⊙DG
* H = (AB) x ⊙DG (180.48,-1.83)
line: (DH)

Euclidea 3.5: Circle through Point Tangent to Line

A C D F G E H

* A: given (0.00,-100.00)
* C: given (-66.91,74.31)
circle: ⊙AC
circle: ⊙CA
* D = (AB) x ⊙CA (-133.83,-100.00)
line: (CD)
* E = ⊙CA x (CD) (-0.00,248.63)
line: (AE)
* F = ⊙AC x ⊙CA (117.50,45.11)
* G = ⊙AC x ⊙CA (-184.42,-70.79)
line: (FG)
* H = (AE) x (FG) (-0.00,0.00)
circle: ⊙HA

Euclidea 3.6: Midpoints Through Trapezoid Bases

A B D C E F

* A: given (-22.40,76.00)
* C: given (75.10,-34.40)
line: (AC)
* B: given (68.40,76.00)
* D: given (-99.10,-34.40)
line: (BD)
* E: given (61.11,196.20)
* F = (AC) x (BD) (11.01,38.17)
line: (EF)

Euclidea 3.7: Angle of 45°

A B C D E

* A: given (0.00,0.00)
* B: given (100.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (50.00,-86.60)
line: (BC)
* D = ⊙BA x (BC) (150.00,86.60)
circle: ⊙DA
* E = (BC) x ⊙DA (236.60,236.60)
line: (AE)

Euclidea 3.8: Lozenge

A B C D E F G H I

* A: given (0.00,0.00)
* B: given (165.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (82.50,-142.89)
* D = ⊙AB x ⊙BA (82.50,142.89)
line: (CD)
* E = (AB) x (CD) (82.50,-0.00)
circle: ⊙EA
* F = (CD) x ⊙EA (82.50,82.50)
line: (AF)
* G = (CD) x ⊙EA (82.50,-82.50)
line: (BG)
* H = ⊙AB x (AF) (116.67,116.67)
* I = ⊙BA x (BG) (281.67,116.67)
line: (HI)

Euclidea 3.9: Center of Quadrilateral

A B C D E F I G H J K L M

* A: given (-201.00,124.00)
* B: given (176.00,199.00)
circle: ⊙AB
circle: ⊙BA
* E = ⊙AB x ⊙BA (52.45,-164.99)
* F = ⊙AB x ⊙BA (-77.45,487.99)
line: (EF)
* C: given (109.00,-76.00)
* D: given (-132.00,-120.00)
circle: ⊙CD
circle: ⊙DC
* G = ⊙CD x ⊙DC (-49.61,110.71)
* H = ⊙CD x ⊙DC (26.61,-306.71)
line: (GH)
* I = (AB) x (EF) (-12.50,161.50)
* J = (CD) x (GH) (-11.50,-98.00)
line: (IJ)
circle: ⊙IJ
circle: ⊙JI
* K = ⊙IJ x ⊙JI (-236.73,30.88)
* L = ⊙IJ x ⊙JI (212.73,32.62)
line: (KL)
* M = (IJ) x (KL) (-12.00,31.75)

Euclidea 4.1: Double Segment

A B C D E

* A: given (-100.00,0.00)
* B: given (0.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (-50.00,-86.60)
* D = ⊙AB x ⊙BA (-50.00,86.60)
circle: ⊙CD
* E = ⊙BA x ⊙CD (100.00,0.00)

Euclidea 4.2: Angle of 60° - 2

B C D E F

* B: given (123.12,0.00)
* C: given (0.00,121.24)
circle: ⊙BC
circle: ⊙CB
* D = (AB) x ⊙BC (295.92,0.00)
* E = ⊙BC x ⊙CB (166.56,167.25)
line: (DE)
* F = ⊙CB x (DE) (86.40,270.89)
line: (CF)

Euclidea 4.3: Circumscribed Equilateral Triangle

A B C D F E G

* A: given (0.00,0.00)
* B: given (100.00,0.00)
line: (AB)
* C = ⊙AB x (AB) (-100.00,0.00)
circle: ⊙CA
* D = ⊙AB x ⊙CA (-50.00,86.60)
* E = (AB) x ⊙CA (-200.00,0.00)
line: (DE)
* F = ⊙AB x ⊙CA (-50.00,-86.60)
line: (FE)
line: (AD)
* G = (FE) x (AD) (100.00,-173.21)
line: (BG)

Euclidea 4.4: Equilateral Triangle in Circle

B C D E F G H I

* C: given (79.62,60.50)
* B: given (100.00,0.00)
circle: ⊙CB
* D = ⊙AB x ⊙CB (26.79,96.34)
circle: ⊙BD
* E = ⊙CB x ⊙BD (100.00,121.00)
circle: ⊙EB
* F = ⊙BD x ⊙EB (204.79,60.50)
line: (BF)
* G = ⊙BD x ⊙EB (-4.79,60.50)
line: (BG)
* H = ⊙AB x (BF) (-50.00,-86.60)
* I = ⊙AB x (BG) (-50.00,86.60)
line: (HI)

Euclidea 4.5: Cut Two Rectangles

A C B D E G F H I J

* A: given (119.88,-11.01)
* B: given (282.12,-78.99)
line: (AB)
* C: given (282.12,-11.01)
* D: given (119.88,-78.99)
line: (CD)
* E: given (-189.77,-68.90)
* F: given (-260.23,-243.10)
line: (EF)
* G: given (-137.90,-120.77)
* H: given (-312.10,-191.23)
line: (GH)
* I = (AB) x (CD) (201.00,-45.00)
* J = (EF) x (GH) (-225.00,-156.00)
line: (IJ)

Euclidea 4.6: Square Root of 2

A B D C E F

* A: given (-80.00,0.00)
* B: given (0.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = (AB) x ⊙BA (80.00,0.00)
circle: ⊙CA
* D = (AB) x ⊙AB (-160.00,0.00)
circle: ⊙DB
* E = ⊙CA x ⊙DB (-40.00,105.83)
circle: ⊙AE
* F = (AB) x ⊙AE (33.14,0.00)

Euclidea 4.7: Square Root of 3

A B C D E

* B: given (0.00,0.00)
* A: given (-80.00,0.00)
circle: ⊙BA
* C = (AB) x ⊙BA (80.00,0.00)
circle: ⊙CB
* D = ⊙BA x ⊙CB (40.00,-69.28)
circle: ⊙AD
* E = (AB) x ⊙AD (58.56,0.00)

Euclidea 4.8: Angle of 15°

A B C D E

* A: given (0.00,0.00)
* B: given (100.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = (AB) x ⊙AB (-100.00,0.00)
circle: ⊙CA
* D = ⊙AB x ⊙CA (-50.00,-86.60)
line: (BD)
* E = ⊙BA x (BD) (186.60,50.00)
line: (AE)

Euclidea 4.9: Square by Opposite Midpoints

A B C D E H G F I J

* A: given (-75.00,0.00)
* B: given (75.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (0.00,-129.90)
line: (AC)
* D = ⊙AB x (AC) (-150.00,129.90)
line: (BD)
* E = ⊙BA x (BD) (-54.90,75.00)
circle: ⊙EB
* F = ⊙BA x ⊙EB (75.00,150.00)
line: (BF)
* G = ⊙AB x ⊙EB (-204.90,75.00)
line: (EG)
* H = ⊙BA x (BD) (204.90,-75.00)
* I = ⊙BA x ⊙EB (-54.90,-75.00)
line: (HI)
circle: ⊙EA
* J = ⊙AB x ⊙EA (-75.00,150.00)
line: (AJ)

Euclidea 4.10: Square by Adjacent Midpoints

A B G I C D E F H J

* A: given (0.00,75.00)
* B: given (75.00,0.00)
line: (AB)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (-27.45,-27.45)
* D = ⊙AB x ⊙BA (102.45,102.45)
line: (CD)
* E = (AB) x (CD) (37.50,37.50)
circle: ⊙EA
* F = (CD) x ⊙EA (75.00,75.00)
line: (AF)
line: (BF)
circle: ⊙AF
* G = (AB) x ⊙AB (-75.00,150.00)
* H = (AF) x ⊙AF (-75.00,75.00)
line: (GH)
* I = (AB) x ⊙BA (150.00,-75.00)
* J = (CD) x (GH) (-75.00,-75.00)
line: (IJ)

Euclidea 4.11: Square by Two Vertices

A B C G E D F H I J

* A: given (-75.00,-75.00)
* B: given (75.00,-75.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (0.00,-204.90)
circle: ⊙CA
* D = ⊙BA x ⊙CA (150.00,-204.90)
circle: ⊙DA
* E = ⊙AB x ⊙CA (-150.00,-204.90)
circle: ⊙EB
* F = ⊙DA x ⊙EB (0.00,7.23)
circle: ⊙CF
* G = ⊙AB x ⊙BA (0.00,54.90)
* H = ⊙AB x ⊙CF (54.90,0.00)
circle: ⊙GH
* I = ⊙AB x ⊙GH (-75.00,75.00)
* J = ⊙BA x ⊙GH (75.00,75.00)

Euclidea 4.11: Square by Two Vertices, variant

A B C D F E G H I J

* A: given (-75.00,0.00)
* B: given (75.00,0.00)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (0.00,-129.90)
* D = ⊙AB x ⊙BA (0.00,129.90)
circle: ⊙CD
* E = ⊙BA x ⊙CD (225.00,0.00)
circle: ⊙EA
* F = ⊙AB x ⊙CD (-225.00,0.00)
circle: ⊙FB
* G = ⊙AB x ⊙EA (-37.50,-145.24)
circle: ⊙FG
* H = ⊙BA x ⊙FB (37.50,145.24)
circle: ⊙EH
* I = ⊙FG x ⊙EH (0.00,-75.00)
* J = ⊙FG x ⊙EH (0.00,75.00)

Euclidea 5.1: Parallel Line

A C D E F

* A: given (-100.00,0.00)
* C: given (0.00,79.00)
line: (AC)
circle: ⊙AC
* D = (AB) x ⊙AC (-227.44,0.00)
* E = (AC) x ⊙AC (-200.00,-79.00)
circle: ⊙DE
* F = ⊙AC x ⊙DE (-200.00,79.00)
line: (CF)

Euclidea 5.2: Parallelogram by Three Vertices

A B C E D G F

* A: given (-100.00,0.00)
* B: given (100.00,0.00)
circle: ⊙AB
* C: given (-80.00,80.00)
circle: ⊙AC
* D = (AC) x ⊙AC (-120.00,-80.00)
circle: ⊙BD
* E = (AB) x ⊙AB (-300.00,0.00)
circle: ⊙CE
* F = ⊙AB x ⊙CE (76.47,-94.12)
line: (BF)
* G = ⊙AC x ⊙BD (-120.00,80.00)
line: (CG)

Euclidea 5.3: Line Equidistant from Two points - 1

A C B D E

* A: given (-100.00,0.00)
* B: given (0.00,79.00)
line: (AB)
circle: ⊙AB
* C: given (-275.10,0.00)
* D = (AB) x ⊙AB (-200.00,-79.00)
circle: ⊙CD
* E = ⊙AB x ⊙CD (-200.00,79.00)
line: (BE)

Euclidea 5.4: Line Equidistant from Two points - 2

A B E C D F

* A: given (-100.00,-35.00)
* B: given (87.30,35.00)
line: (AB)
circle: ⊙AB
circle: ⊙BA
* C = ⊙AB x ⊙BA (54.27,-162.21)
* D = ⊙AB x ⊙BA (-66.97,162.21)
line: (CD)
* E: given (235.00,0.00)
* F = (AB) x (CD) (-6.35,0.00)
line: (EF)