Cyclic Quadrilateral
Calculator and formulas for calculation of cyclic quadrilateral properties
This function calculates the properties of a cyclic quadrilateral. A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle.
For calculation enter the lengths of the four sides. Then click on the 'Calculate' button.
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Description
A cyclic quadrilateral is a quadrilateral whose vertices lie on the circumference of the quadrilateral. This means that all sides of the cyclic quadrilateral are chords of the circumference. In general, the term “chord quadrilateral” refers to a non-overlapping chord quadrilateral, which is therefore convex.
In the cyclic quadrilateral, the sum of the opposite angles is 180°.
Formulas
Diagonal (e)
\(\displaystyle e =\sqrt{\frac{(a·c+b·d)·(a·d+b·c)}{a·b+c·d}} \)
Diagonal (f)
\(\displaystyle f =\sqrt{\frac{(a·b+c·d)·(a·c+b·d)}{a·d+b·c}} \)
Area(A)
\(\displaystyle A= \frac{e·(a·b+c·d)}{4·r}\)
\(\displaystyle A= \frac{f·(a·d+b·c)}{4·r}\)
\(\displaystyle A= \sqrt{(s-a)·(s-b)·(s-c)·(s-d)}\)
\(\displaystyle s=\frac{a+b+c+d}{2}\)
Perimeter (P)
\(\displaystyle P=a+b+c+d\)
Circumcircle radius (r)
\(\displaystyle r=\frac{1}{4·A}·\sqrt{(a·b+c·d)·(a·c+b·d)·(a·d+b·c)} \)
Angle (α)
\(\displaystyle α=arccos\left(\frac{a^2+d^2-b^2-c^2}{2·(a·d+b·c} \right)\)
Angle (δ)
\(\displaystyle δ=arccos\left(\frac{d^2+c^2-a^2-b^2}{2·(d·c+a·b} \right)\)
Angle (β)
\(\displaystyle β=180°-δ\)
Angle (γ)
\(\displaystyle γ=180°-α\)
Square • Rectangle • Golden Rectangle • Rectangle to Square • Rhombus, given varios parameter • Rhombus , given diagonal e, f • Parallelogram, given 2 sides and angle • Parallelogram area, given side and height • Trapezoid • Cyclic Quadrilateral • General Quadrilateral • Concave Quadrilateral • Arrowhead Quadrilateral • Crossed Square • Frame • Kite, given 2 diagonal and distance • Kite Area, given 2 diagonal • Half Square Kite • Right Kite"
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