GSP4\QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$ Lincircle` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' At@U@@Bm@`|@@ @C@|@,@, - I  / / /   -   -   -    \QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$4 Lexcircle` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' As@I@@B0q@o@@ @ @ @ @ @C@n@,@/ ,/   -  I[a] /   -  @  /  /   -  -         4\QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$D Lexcircles` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' `v@@e@@0s@t@@ @ @ @ @ @~@t@,@/ ,/   -   /   -  @  /  /   -  - @  ,/ ,/  - /  - @  / /  -  - @  ,/ ",/ $ - #% / &' - '(/ &!/ & - !* - + - "/ ./ .'/ .  -  1 - '0 - / .3   ,  -  Q C-),Q CQ C   &-   @ ? A\QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$D"LFeuerbach theorem` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' Au@P@@Bk@}@@ @C@~@,@, - I  / / /   -   -   -           /  /  - N @   - F   > 0     \nQ\aACFeuerbach theorem: The nine-point circle is tangent to the incircle\QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$1]LFeuerbach theorem` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' `t@m@@@q@u@@ @ @ @ @ @ ~@u@,@/ ,/   -   /   -  @  /  /   -  - @  ,/ ,/  - /  - @  / /  -  - @  ,/ ",/ $ - #% / &' - '(/ &!/ & - !* - +   ,  -  Q C-),Q CQ C  '    87 :/ ;: 98 =/ >= - <? @8 @ - B6 @& - D4 @  - F5 97 A> @GCEDBF978=:H@AI   PnQ\aA7The nine-point circle is also tangent to the excircles. -n  /n K/n K /n K' -n 'N -n  M -n Ln KP@ n @K -n SR nR> n UROQTPK   'N"nQ\aAincirclepn n &,n  n  nW nX nY