How to construct a bicentric quadrilateral

Nikol Dimitrova shared this question 2 weeks ago
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A bicentric quadrilateral ABCD is inscribed in the circle k_1(O_1; R) and circumscribes the circle k_2(O_2; r). How to construct it in GeoGebra?

Comments (10)

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try with attached (use navigation bar)

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I don't want the quadrilateral to be a rectangle.

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per ottenere un quadrato inscritto in un cerchio di raggio R >>> l=R/sqrt(2) (l=lato del quadrato)

to obtain a square inscribed in a circle of radius R >>> l = R / sqrt (2) (l = side of the square)1a76350441fd345b8904cabcab1a9c93

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en la practica dados dos circulos es imposible encontrar tal cuadrilatero; dado un circulo sí es posible encontrar otro circulo para el cual existe el cuadrilatero


en el adjunto mueve E and or D until distance=0

esto es solo una aproximacion numerica que te dara idea de la gran dificultad de la cuestion

Files: foro.ggb
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idea?

W.F.

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another idea?

UmInKreis


W.F.

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dados dos circulos que tienen un cuadrilatero bicentrico entonces hay infinitos cuadrilateros para esos circulos ; por lo tanto si es posible sirve cualquiera y si no es posible no se encontrará

https://en.wikipedia.org/wi...

dado un circulo se puede construir otro circulo donde los cuadrilateros ciclicos son bicentricos

https://en.wikipedia.org/wi...

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Here's a solution for a general polygon from 2015 :)


https://www.geogebra.org/m/TqXB8SvT

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As mathmagic says - once you have two correct circles then it's easy

  • start with a point on the outer circle
  • construct the tangent to the inner circle
  • intersect with the outer circle
  • repeat another 3 times

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Interestingly this one is much easier to construct than the others as you can just use the "Conic through 5 points" Tool https://www.geogebra.org/m/mkW2vCez

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