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.o$76Lisogonal line and reflections` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' Ao@U@@Bd@y@@  @/@ @C@y@@ @ 4@?  ?  /  /   -  H /  - O P@t@ p@"@ Pbn" Pcn"    ," @     8?Q   -   <-><->><-><->>>eF<:!&>>>>>>>>>>>>!  > &%$   NnQ\aAProofn88c$c| n z^B]?n )n),+) - ,*Q C+-)R D.  !3? 00,20 - 31Q C240R D5\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.o$7`Lisogonal conjugate` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial  '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' A@o@U@@Bd@y@@  @/@ @C@y@@ @ 4@?  ?  /  /   -  H /  - O P`u@r@"@ P[b]" P[c]" P[a]   ," @    - <:!&>>>>>>>>>>>>!  ?  ,,?   -  %?   - "'" &#?  )" ($?  + - *,Q - - -  - -  2liV? 44-,64 - 75Q C684R D9  Z';? ;;,=; - ><Q C=?;R D@   ?? BB-,DB - ECQ CDFBR DG  pZ&? II,KI - LJQ CKMIR DN,,<0><0>>f  - R йN ? SS-,US - VTQ CUWSR DX Q kf? ZZ,\Z - ][Q C\^ZR D_\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.o$#LO and H` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial  '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' `f@z@@@z@@  @/@ @q@@Q@@ @ 4@?  ?  /  /   -  H /  - O     >? , - Q CR D  :^? , - Q C R D!88 /% /H\QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.o$%"Lreflections of H on circumcircle` 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':' Bd@@x@@C@@x@@  @/@ @Ap@8@@ @ 4@?  ?  /  /   -  H /  - O   " Obi" Oci" Oai    DBon/<0>>on1 >    NnQ\aA4circle of reflections of O congruent to circumcircle"n Hbc" Hcc" Hac    !> # $!"   >nQ\aA$Reflections of H lie on circumcirclet\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.o$7TLpedal circle` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial  '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' An@[@@Bc@pz@@  @/@ @C@pz@@ @ 4@?  ?  /  /   -  H /  - O Ps@q@"@ Pb" Pc" Pa   ," @    - <:!&>>>>>>>>>>>>!  ?  ,,?   -  %?   - "'" &#?  )" ($?  + - *,P*  - -" -" -" - -1 -2 -3 - 1 - 3 3 -> <;9:   \NnQ\aA5The circles of reflections of P and P* are congruent./n  /n "/n   -n "? -n  > -n  @n Cn Bn A/n - /n -"/n -  -n "H -n  G -n  In -Ln -Kn -J n<M PK PC PL> @BAJLCPQDMOFE<RS   TnQ\aA;P and P* have a common pedal circle with midpoint as center\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.o$/Lnine-point circle` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0488/Oct 31 20010#` Arial  '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' j@z@@h@z@@  @/@ @@r@W@@ @ 4@?  ?  /  /   -  H /  - O ?  /  / /   -  -   -     /  / /   -  -   -   " !    &N '    - +( - )( - *(> -.,+*)   c*nQ\aANine-point circle