Una vez descritos los distintos ángulos existentes en un polígono, estudiaremos un cuadrilátero especial,[br]denominado cuadrilátero cíclico.[br][br]Si en una circunferencia marcamos cuatro puntos y dibujamos el polígono formado por ellos, obtendremos un cuadrilátero denominado cíclico.[br][br][img 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GnRRRQAUUUUAFFFFADJI1ljaN1DIwwykcEVkQBrC4GnzMWQgm2kJ+8o6qfcfqPxraqtfWaXtsYnYqQdyOvVGHQipa7FRdtGQ0VXtLh5Q8NwoS5hO2VR0Pow9j/9arFSUFFFFMAooooAKKKKACiiorq4W1tZbhxkRqWx6nsKAQ21X7Vq7ydY7Ndi/wDXRhk/kMD8TWtVPS7VrSwjjk5lbLyn1duT+tXKcdiZO7CiiiqJCiimSSJFG0kjBUQFmJ7AUAZi/wCleKHfqljbbPo8hyf0UfnRS+H0d9Pa+lUrJfSNcEHqFPCD8FC0UAalZMh/s3xAkvSDUgI2PZZlHy/99LkfVR61r1U1KxXUbGS2LFGPMcg6xuOVYe4IBoAtUtUdJv2vrLdMojuYmMVxH/dkHX8D1HsRV6gAooooAKKKKACkpaKAM/UrSR9l5agfaYRwucCVe6H+noaZbzx3MCzRElW9eoPcH3FaRrIvY/7OuGvUH+jSn/SVH8B/56D+v51ElbUuLvoWaKKKBhRRRQAUUUUAFVZV+16lbWnVIz9ol+gPyj8W5/4DVrIAyTgDqaZoyGSGS+YfNdtuX2QcKPy5/Glu7D2VzRpaKK0MgooooASsrW2N0YNIjPzXjfvcfwwry5/Hhf8AgVackiRRtJIwVEBZmJwAB1NZmio9082sTqVe7AEKt1jhH3R7E8sfqPSgDVUAAADAHQCilooAKSlooAxtTB0q9/tmNSYGUJfIB/AOkn1Xv/s/QVrqyuoZWDKwyCDkEUpUMCGAIPBB71iW7HQLpLGQn+zp2xayH/lgx/5ZE+h/hP4elAG5RSUtABRRRQAUUUUAJSMgZSrAEEYIPQ06igDFjU6bdLZOSbeTP2Zz29Yz9O3t9Kt1Pd2kV7bNBKDg8hhwVI6Ee4rPtJ5Cz2tzgXMP38cB17OPY/oaztZmid1cs0UUUwCiiigCpqO6WOOyjOHu38vI7J1c/l/OthFVECKAFUYAHYVl6cv2nUri7PKQ/wCjxfXq5/PA/wCA1qiiPcU+wtFFFWQFJmlrN1S/ljkTT7Da19OMrkZEKd5G9h2Hc8etAFe9b+2NQ/sqMk2sBD3rjoe6xfj1Ptgd62QMVW0+wh020W3hycEs7sctIx5LMe5Jq1QAUUUUAFFFFABUVzbw3dvJb3EayRSLtZGHBFS0UAYtvczaNMllqMrSWztttrx/0jkP970bv9euzTJ4IrmF4J41kikG1kcZDD0IrI/0vQeCJbzTB0Iy01sP5un6j3oA26Kit7mG7gSe3lWWJxlXQ5BqWgAooooAKKKKAEqjqVk86pcW2Fu4OYyejDuh9j+hwav0hpNXGnZ3My1uUu7dZkBXOQyt1Rh1U+4qWq+oQNY3DajCpMTAC6jHoOjgeo7+o+lTqwZQykFSMgjoRUeRp5oWoL24a1tHlQbpOFjX1cnCj8zU9Vgn2vWI4usdovmv7uchR+AyfyoYIv2FqLKyitwd2xeW/vHufxOasUUtWjLcKSisebVJ7+ZrPRQrsp2y3jDMUJ7gf329hwO57UwLGo6m0Eq2VnGLi/lGUjJ+VB/fc9lH5noKfpunCwjdnkM91Md087DBkb+gHQDsKdp+mwadEyxlnkkO6WaQ5eVvVj/ToO1W6AFooooAKKKKACiiigAooooAKSlooAybjR2iuHvNKnFncOcyJt3QzH/aXsf9oYP1oi1wQSLBq0BsJicK7HdDIf8AZfp+Bwa1qZJGk0ZjkRXRhhlYZB/CgBwORmlrJOiNa/NpN5JZf9MSPMh/74P3f+AkUC/1W14vdM85R/y1sn3A/wDAGwR+GaANais2LxBpUknlm9SGT/nnODE35Ng1oI6yKGRgynoQcg0AOpKWkoAMZ61jCP8Asu7Fuf8Aj0nb9wf+ebd0+h6j8vStmobq3iu7Z4JhmNxz2x7j0IqZK5UXYrO6xRtI52qgLMfQCjR4WSzNxKMTXTGVwe2fuj8BgVws/jC5mg2vaxzaej/vJQ5Es0Sty2MYGQOma7Ndbku41bS9NuLlXUFZJB5MeD7tz+Qq5UZws5q1wclayNaqN7rNrZSi3y9xdN922gXfIfw7D3OBVf7Bqd6f+JhqAhj7wWWVz9ZD8x/DbV6ysLTT4jFaQJEpOTtHLH1J6k+5pEmebC/1bnVXFvan/lygflh/00cdf91ePc1rRRRwRLFDGscaDCoowAPQCn0UAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQBHNbw3EZjniSVD1V1DD8jWc3hrSC5eO0Fu5/it3aI/wDjpFatFAGV/YKr/q9T1OP/ALei/wD6Fmj+xZ/+g5qf/fUf/wARWrRQBlf2GT9/V9Tb/tuF/wDQQKQ+GtNk/wCPhbi69ri5kkH5E4rWooA4yT4dQNcNHHqMkensT/owjG5VPVA/YfhkCug1pmtdCm+zs0RRVVChwVGQOPwrTrK8THHh28I6hQR/30K2jOdScVJ3FaxG8c2l3tpsvLieK4l8p4523diQQe3StiuQ8I3M+qXck99K88kA/dlz93PXiuvp4iLhPle6Bai0UUVgMKKKKACiiigAooooA//Z[/img][br][br]Llamaremos cuadrilátero cíclico a aquél que se puede inscribir en una circunferencia. El cuadrilátero que hemos construido lo es; pero ¿son cíclicos todos los cuadriláteros? ¿Qué condición se ha de cumplir para que un cuadrilátero sea cíclico? [br][br]Seleccionamos la herramienta [b][i]Ángulo  [/i][/b][url=https://wiki.geogebra.org/es/Herramienta_de_%C3%81ngulo][img width=24,height=24]data:image/png;base64,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[/img][/url] y creamos los cuatro ángulos interiores del cuadrilátero. Para ello, una vez seleccionada la herramienta, señalaremos tres vértices consecutivos del cuadrilátero, en el sentido de las agujas del reloj, para construir el ángulo formado en el segundo de los vértices marcados.[br][br][img 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[/img][br][br]Comprobamos la suma de los ángulos opuestos α+ γ y β+ δ.[br][br]

Podemos observar que al mover los vértices del cuadrilátero, la suma de los ángulos opuestos se mantiene[br]constante, siendo igual a 180⁰.[br][br]Por tanto, esta será la condición para que cualquier cuadrilátero pueda ser cíclico.