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2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, N-gon

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Rhombus, Parallelogram, Kite, Right Trapezoid, Isosceles Trapezoid, Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Antiparallelogram, House-Shape, Concave Pentagon, Parallelogon, Threestar, Fourstar, Pentagram, Hexagram, Oktagram, Star of Lakshmi

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Round Corner, Annulus, Annulus Sector, Ellipse, Elliptical Segment, Stadium, Digon, Spherical Triangle, Reuleaux Triangle, Cycloid, Astroid, Hypocycloid, Cardioid, Parabolic Segment, Arbelos, Salinon, Lune, Oval, Three Circles, Lemniscate, Squircle
3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:
Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Rhombic Triacontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Snub Disphenoid

Other Polyhedrons:
Cuboid, Square Pillar, Square Pyramid, Regular Pyramid, Pyramid, Regular Frustum, Frustum, Bipyramid, Ramp, Right Wedge, Wedge, Rhombohedron, Parallelepiped, Prism, Oblique Prism, Antiprism, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Half Cuboid, Truncated Rhombohedron, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron

Round Forms:
Sphere, Hemisphere, Cylinder, Cut Cylinder, Oblique Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Spheroid, Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Wedge, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Spherical Shell, Cylindrical Shell, Spherical Ring, Torus, Arch, Reuleaux-Tetrahedron, Capsule, Lens, Barrel, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids


Cyclic Quadrilateral Calculator

Calculations in a cyclic quadrilateral. A cyclic quadrilateral is a quadrangle whose vertices lie on a circle, the sides are chords of the circle. Enter the four sides (chords) a, b, c and d, choose the number of decimal places and click Calculate. Angles are calculated in degrees, here you can convert angle units.

Ptolemy Side a: Cyclic Quadrilateral
Side b:
Side c:
Side d:
Diagonal e:
Diagonal f:
Angle at A (α):
Angle at B (β):
Angle at C (γ):
Angle at D (δ):
Perimeter (p):
Circumcircle radius (rc):
Area (A):
Round to    decimal places.

e = √ (ac+bd) * (ad+bc) / (ab+cd)
f = √ (ab+cd) * (ac+bd) / (ad+bc)
a * c + b * d = e * f (Ptolemy's theorem)
α = arccos( (a²+d²-b²-c²) / (2*(ad+bc)) )
δ = arccos( (d²+c²-a²-b²) / (2*(dc+ab)) )
β = 180° - δ
γ = 180° - α
p = a + b + c + d
Semiperimeter s = p / 2
A = √ (s-a) * (s-b) * (s-c) * (s-d)
rc = 1/(4*A) * √ (ab+cd) * (ac+bd) * (ad+bc)

Side lengths, diagonals, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).


The center of the circle is at the intersection of two perpendicular bisectors. These can be constructed by drawing intersecting circles around two neighboring vertices and connecting their intersections.

Cyclic quadrilateral, perimeter and area
perimeter p, area A
Cyclic quadrilateral, sides and angles
sides and angles

Cyclic quadrilateral, radius and circumcircle
radius and circumcircle
Cyclic quadrilateral, perpendicular bisectors
perpendicular bisectors



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