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Conceptos Clave

La Circunferencia

Como ya se mencionó, la circunferencia es una línea curva cerrada cuyos puntos están todos a la misma distancia de un punto fijo llamado centro. Sus elementos principales son:

  • Centro: Es el punto que se encuentra a la misma distancia (es equidistante) de todos los puntos de la circunferencia.
  • Radio: Es el segmento que une el centro de la circunferencia con cualquiera de sus puntos.
  • Diámetro: Es el segmento que une dos puntos extremos de la circunferencia, pasando por el centro. Cabe notar que el diámetro el doble del radio.

circunferencia Tenor. (2021). Circunferencia gif. Recuperado de https://c.tenor.com/sB6YqeJTynkAAAAM/circunfer%C3%AAncia.gif 

Forma General de la Circunferencia

Hay un caso particular de circunferencia, que tiene su centro en el origen. La ecuación que la define se llama ecuación canónica de la circunferencia:

x2+y2=r2

Si la circunferencia no está centrada en el (0,0), es posible armar un nuevo sistema de modo tal que el centro de la circunferencia (h,k) coincida con el nuevo origen de coordenadas. De forma que se obtiene la siguiente ecuación:

 (x-h)2+(y-k)2=r2

Aquí, el centro está dado por:

C (h , k)

La ecuación anterior se conoce como ecuación ordinaria de la circunferencia. Para obtener la ecuación general debemos desarrollar los binomios al cuadrado, por tanto, la ecuación de la circunferencia se puede escribir de la siguiente manera:

  x2 + y2 +Dx + Ey + F = 0

La cual se conoce como la ECUACIÓN GENERAL de la circunferencia.

Otros elementos de la circunferencia

En este tema de circunferencia también es necesario mencionar algunos otros elementos y características como:

  • Cuerda: Es el segmento que une dos puntos de la circunferencia, pero a diferencia del diámetro no pasa por el centro de la figura.

cuerda

  • Arco: Es la curva que une los dos extremos de una cuerda, como la porción de la circunferencia de abajo que une los puntos A y D.

arco

  • Ángulo central: Es el ángulo que se forma entre dos radios de la circunferencia.

ang central

  • Semicircunferencia: Es la porción de la circunferencia delimitada por dos extremos del diámetro.

semiscircun

  • Tangente a la circunferencia: Es La recta corta a la circunferencia en un punto

tangente

Celeberrima. (2021). Definición de círculo y sus partes. Recuperado de https://www.celeberrima.com/definicion-de-circulo-y-sus-elementos-o-partes/

Interacción de recuperación del aprendizaje

2

Observa la descripción e identifique y rellene las palabras que faltan para formar el concepto

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