{"id":11,"date":"2012-09-29T09:52:40","date_gmt":"2012-09-29T14:52:40","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/malarco\/?p=11"},"modified":"2012-09-29T09:58:26","modified_gmt":"2012-09-29T14:58:26","slug":"posiciones-relativas-de-dos-circunferencias","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/malarco\/2012\/09\/29\/posiciones-relativas-de-dos-circunferencias\/","title":{"rendered":"Posiciones Relativas de dos Circunferencias"},"content":{"rendered":"

 <\/p>\n

Dadas dos\u00a0circunferencias<\/a>\u00a0C<\/em>1<\/span>\u00a0y\u00a0C<\/em>2<\/span>\u00a0de\u00a0radios<\/a>\u00a0r<\/em>1<\/span>\u00a0y\u00a0r<\/em>2<\/span>\u00a0y cuyos centros\u00a0O<\/em>1<\/span>\u00a0y\u00a0O<\/em>2<\/span>\u00a0est\u00e1n a una\u00a0distancia<\/a>\u00a0d<\/em>, entonces la posici\u00f3n relativa de\u00a0C<\/em>1<\/span>(O<\/em>1<\/span>,\u00a0r<\/em>1<\/span>) y\u00a0C<\/em>2<\/span>(O<\/em>2<\/span>,\u00a0r<\/em>2<\/span>)<\/span>\u00a0puede ser:<\/span><\/p>\n

Exteriores:<\/strong>\u00a0las dos\u00a0circunferencias<\/a>\u00a0no tienen\u00a0puntos<\/a>\u00a0comunes.<\/span><\/p>\n

\n\n\n\n\n
\n
\"\"<\/span><\/div>\n<\/td>\n<\/tr>\n
\n
d<\/em><\/span>\u00a0> r1<\/span>\u00a0+ r2<\/span><\/span><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

<\/p>\n

Tangentes exteriores:<\/strong>\u00a0las dos\u00a0circunferencias<\/a>\u00a0tienen un\u00a0punto<\/a>\u00a0en com\u00fan y sus centros\u00a0O<\/em>1<\/span>\u00a0y\u00a0O<\/em>2<\/span>\u00a0est\u00e1n en\u00a0semiplanos<\/a>\u00a0diferentes respecto de la\u00a0recta tangente<\/a>\u00a0com\u00fan.<\/span><\/p>\n

\n\n\n\n\n
\n
\"\"<\/span><\/div>\n<\/td>\n<\/tr>\n
\n
d<\/em><\/span>\u00a0= r1<\/span>\u00a0+ r2<\/span><\/span><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Tangentes interiores:<\/strong>\u00a0las dos\u00a0circunferencias<\/a>\u00a0tienen un\u00a0punto<\/a>\u00a0com\u00fan y sus centros\u00a0O<\/em>1<\/span>\u00a0y\u00a0O<\/em>2<\/span>\u00a0est\u00e1n en el mismo\u00a0semiplano<\/a>\u00a0respecto de la\u00a0recta tangente<\/a>\u00a0com\u00fan.<\/span><\/p>\n

\n\n\n\n\n
\n
\"\"<\/span><\/div>\n<\/td>\n<\/tr>\n
\n
d<\/em><\/span>\u00a0= r1<\/span>\u00a0- r2<\/span><\/span><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Secantes:<\/strong>\u00a0las dos\u00a0circunferencias<\/a>\u00a0tienen dos\u00a0puntos<\/a>\u00a0comunes.<\/span><\/p>\n

\n\n\n\n\n
\n
\"\"<\/span><\/div>\n<\/td>\n<\/tr>\n
\n
\n

r1<\/span>\u00a0- r2\u00a0<\/span><\/em><\/span><\/span>< d\u00a0<\/em><\/span>< r1<\/span>\u00a0+ r2<\/span><\/span><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

Circunferencia interior:<\/strong>\u00a0las dos\u00a0circunferencias<\/a>\u00a0no tienen\u00a0puntos<\/a>\u00a0comunes estando los puntos de\u00a0C<\/em>2<\/span>(O<\/em>2<\/span>,\u00a0r<\/em>2<\/span>)<\/span>\u00a0en el interior de\u00a0C<\/em>1<\/span>(O<\/em>1<\/span>,\u00a0r<\/em>1<\/span>).<\/span><\/p>\n

\n\n\n\n\n
\n
\"\"<\/span><\/div>\n<\/td>\n<\/tr>\n
\n
d<\/em><\/span>\u00a0< r1<\/span>\u00a0- r2<\/span><\/span><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n<\/div>\n

Conc\u00e9ntricas:<\/strong>\u00a0caso particular de las circunferencia interior, cuando tienen el mismo centro.<\/span><\/p>\n

\n\n\n\n\n
\n
\"\"<\/span><\/div>\n<\/td>\n<\/tr>\n
\n
d<\/em><\/span>\u00a0= 0<\/span><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Los \u00faltimos tres casos no pueden presentarse cuando los radios tienen la misma medida r1<\/span>\u00a0= r2<\/span><\/span><\/p>\n<\/div>\n