ZXTape! 0Created with Ramsoft MakeTZX2o#'O' Level Maths Revision - Geometry Rose Software1984English EducationalFullNoneOriginal Releaseg4 qqPXs 32743 b23613=\+256*23614>\,0:23613=\+1+256*23614>\,0 7:7:7::9 ;0,0;" Program loading ";0,18;1;" PLEASE WAIT ";0:0,0;:"sc":1:1:1:0,0;:"gr""s",24:0,0;:"4": sc @q           88     8?88;?88 8            @     ||@~<<~B<>?   88     8?88;?88 8   ?  B    H  B8<8h88x<B@@B@@BB           88     888;888     !       B    H  B DD TD<0DDB@|B<|BB           8?;;8   ??>;?8?  &0    2   0"   ! (  | DD ??;;8   ;8     0      ?@ 8              8  8      8|8888888                    ""  88           ?88   8|88;888        ?      $B   0  ! $B   $   $   D [     UJk5R      $T*Q$Y|     ddD!DIE""&&    / &$D"$Ad0    @D"!D"! Aa    # $@  ? >    mv      ꔫ5)Wh    ?$I)($   BI"IDB!8    |0!H  >  ?`DB!B" s    / $P    ? 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";k:"0","48":"55","0":"0","39":"55","0" nAv=v+"1":װ".5","-10":װ"1.5","-20":"19","0";a$::"120" t9۰"1":"17","8";" * WELL DONE * ":۰"0":u=u+"1" w<װ".2","2":װ".2","2":װ".2","4":װ".2","4":װ".5","9" xV"19","0";a$:a$="":"9000":"3":ڰ"3"::"3","7";;" TOTAL CORRECT:  ";u y"6","7";" TOTAL INCORRECT: ";v:"56","152":"135","0":"56","143":"135","0":"56","128":"135","0":"56","119":"135","0":122z+qu z"9000":ڰ"5":"5":: }H"16","6";"MORE EXAMPLES? y OR n":"0":q$=:q$"y"q$"n""125" q$="y""5":ڰ"5":: "200":"0","14";" END ";"21","9";"Press any key":"112","175":"40","0":"0","-8":"-40","0":"0","8":0:"6" Jٰ"2":ڰ"7":"7"::"98","126":"60","-60":"98","66":"60","60" ^30,-30,-:-30,-30,-:-30,-30,-:-30,30,- ѡ-30,30,-:30,30,-:30,30,-:30,-30,-:9 :9 ,14;"ROSE";10 ,12 ;"SOFTWARE": ,ڰ"5"::"900":"910":"2","0";"The angle between";"4","0";"the radius of";"6","0";"a circle and a";"8","0";"tangent is ALWAYS ?" /Lp$(1)="90":p$(2)="180":p$(3)="45":a=1:"80" J"900":"920":"930":"7","25";"y";"3","26";"z";"2","0";"y is the angle";"4","0";"at the centre";"6","0";"of the circle";"8","0";" SO:" MFp$(1)="y=2z":p$(2)="z=2y":p$(3)="y+z=90":"80" hE"900":"920":"940":ް"1":"3","26";"z";"3","22";"y":ް"0" k{"2","0";"What is always";"4","0";"true for";"6","0";"y and z?":p$(1)="y=z":p$(2)="yXz=360":"80" 9"900":"920":"950":"3","26";"z";"9","25";"y" q"2","0";"y and z are";"4","0";"opposite s in a";"6","0";"cyclic quadrilateral";"8","0";" SO: " Jp$(1)="y+z=180":p$(2)="y-z=90":p$(3)="y=2z":"80" B"900":"960":"0","25";"A";"11","25";"C";"9","29";"B" "3","0";"AC is a diameter";"6","0";" SO: ":p$(1)="ABC=90":p$(2)="ABC is isosceles":p$(3)="CAB=BCA":80P g"970":"940":"920":"-56","-4":"9","20";"C";"3","26";"z";"1","21";"A";"8","29";"B" s"222","112":-2,-6,/2:i=((*6)+2)*10 :"9","28";"^";"10","28";i;"" M"2","0";"AB is a diameter";"4","0";"and ABC=";i;"";"7","0";"z=?" նp$(1)=(90Z-i)+"":p$(2)=i+"":p$(3)=(i+20)+"":a$=" ACB=90 (angle in semi-circle) SO CAB="+(90Z-i)+" (180 in ABC) = z ":80P K"970":"940":"174","156":"-14","12.5":"174","102":"28","28" "5","25";"O";"0","22";"A";"9","29";"B";"9","20";"C";ް"1";"6","25";"z":ް"0":"170","160":"4",-14,/2 }i=((*7)+11 )*10 :"2","17";i;"";"3","0";"AOB is a";"5","0";"diameter";"8","0";" SO  z=?" p$(1)=(360h-2*i)+"":p$(2)=(i/2)+"":p$(3)=(i-40()+"":a$="CAB=180-"+i+" SO z=2X"+(180-i)+" ( atcentre=twice at circumference)":80P i=((*6)+2)*10 :"980"::"960":ް"1":"3","25";"z";"0","25";"A";"11","24";"C";"8","30";"B":ް"0" V"2","0";"AC is a diameter";"4","0";"TC is a tangent";"7","0";" SO  z=?" p$(1)=i+"":p$(2)=(90Z-i)+"":p$(3)=(i+20)+"":a$="TCA=90( between radius & tgt)and ABC=90 ( in semi-circle) ":80P ;i=((*4)+2)*10 :"920":"950":"980" j=((*4)+6)*10 :ް"1":"11","23";"^";"12","23";"z";"11","20";"S";"4","25";j:ް"0":"190","96":-2,-6, "2","0";"ST is a";"4","0";"tangent.";"7","0";"z=?":p$(1)=(j-i)+"":p$(2)=(100d-i)+"":p$(3)=(j-45-)+"":a$="SUM OF OPP.s OF CYCLIC QUAD=180":80P 0"990":"0","0";" THE ALTERNATE ";1,0;" SEGMENT THEOREM ";"9","20";"B";"7","21";"z";"7","27";"z":"224","107":4,4,- 9"14","0";"The angle z between a chord AB",,,"and a tangent is equal to the",,,"angle z in the alternate segment":9000(# N"995":"950":"11","25";"C";"5","18";"T";"9","20";"D";"2","0";"DAB=";i;"";"4","0";"What is the";"6","0";"value of BDT?" Wp$(1)=(180-i)+"":p$(2)=(195-i)+"":p$(3)=(90Z+i)+"":a$=" BCD=180-"+i+" (opp.s in cyclic quad.) BDT=BCD (alt.seg.th.)":80P Xf"995":"149","130":"-24","28":"104","-50":"9","20";"C";"1","16";"T";"12","24";"S" [j=(*9 )+"10":"218","112":0,-6,/2:ް"1":"10","27";"^";"11","27";j;"";"3","17";"?":ް"0" ^"2","0";"CAB=";i;"";"4","0";"TBC=";j;"";"6","0";" SO  CTB=?":p$(1)=(i-j)+"":p$(2)=(90Z-j)+"":p$(3)=(i-j+5)+"" aSa$=" BCS=CAB="+i+" (alt.seg.th.) SO TCB=180-"+i+" & s in TCB=180" dqu="1":"80":"460" &" REVISION QUESTIONS ":"905": "200,128,12 *: ["248","90":"-88","0":"11","25";"T";"5","25";"O":"202","126":"0","-36": ,"174","102":"40","61":"16","-56": ,"174","102":"27","26":"29","-22": +"174","102":"0","54":"56","-50": ,"174","102":"27","-10":"30","15": 8"200","91":"30","16":"-30","58":"0","-74": N" EXERCISE ":"0","175":"79","0":"0","168":"79","0":"905": "970":"248","90":"-80","0":"212","96":2,-6,-::"11","30";"T";"11","26";"^";"12","26";i;"": ކ"905":"920":"0","26";"A":"174","102":"56","5":"149","130":"48","-56":"170","107":6,1,-/2: "970":"990":2,-5,-/2:i=((*7)+2)*10 :"210","156":6,0,/2:"1","28";"<-";i;"8","30";"B": #("""9000" #+,"21","9";"Press any key":="""9003" #."""9006" #1װ".05","4":: uvaiPkQ1O A890 180 45  g5 qqQMs 32727 b23613=\+256*23614>\,0:23613=\+1+256*23614>\,0 7:7:7::9 ;0,0;" Program loading ";0,18;1;" PLEASE WAIT ";0:0,0;:"sc":1:1:1:0,0;:"gr""q",40(:0,0;:"5": sc @           88     8?88;?88 8            @     ||@~<<~B<>?   88     8?88;?88 8   ?  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";k:"0","48":"56","0":"0","-9":"-56","0":"0","9" nAv=v+"1":װ".5","-10":װ"1.5","-20":"19","0";a$::"120" t9۰"1":"17","8";" * WELL DONE * ":۰"0":u=u+"1" w<װ".2","2":װ".2","2":װ".2","4":װ".2","4":װ".5","9" xS"19","0";a$:a$="":"9000":"3":ڰ"3"::"3","6";" TOTAL CORRECT: ";u y0"6","6";" TOTAL INCORRECT: ";v:"122"+qu z"9000":ڰ"5":"5":: }J"16","5";"MORE EXAMPLES? y OR n":"0":q$=:q$"y"q$"n""125" q$="y""5":ڰ"5":: "200":"0","14";" END ";"21","9";"Press any key":"112","175":"40","0":"0","-8":"-40","0":"0","8":"0":"6" Jٰ"2":ڰ"7":"7"::"98","126":"60","-60":"98","66":"60","60" ^30,-30,-:-30,-30,-:-30,-30,-:-30,30,- ѡ-30,30,-:30,30,-:30,30,-:30,-30,-:9 :9 ,14;"ROSE";10 ,12 ;"SOFTWARE": ,ڰ"5":"5"::"900":212,128,8*:"236","128":"-36","0":"0","2":"212","128":"0","2":"6","24";"O";"6","26";"P";"6","31";"T" /i=((*5)+5)*2:j=(*4)+1:"1","0";"The radius of the";"2","0";"larger circle";"3","0";"centre O = ";i;"cm." 2{"5","0";"The radius of the";"6","0";"smaller circle";"7","0";"centre P = ";i/2+j;"cm.";"9","0";"OP = ?" 5p$(1)=(i/2-j)+"cm":p$(2)=((3*i/2+j)/2)+"cm":p$(3)=(i/2-j+1)+"cm":a=1:a$=" SINCE OP = OT - PT = "+i+"cm-"+(i/2+j)+"cm ":80P J"900":"230","106":"-58","0":"9","25";"P";"5","25";"O";"9","20";"A";"9","29";"B":"202","126":"0","-20" M|"217","104":"0","4":"187","104":"0","4":"2","0";"If AP=PB";"4","0";"then it is";"6","0";"true that:-" Pp$(1)="APO=90":p$(2)="OP=half radius":p$(3)="OP = AP":a$="  OP is called the   perpendicular bisector of AB ":80P h1"900":"910":"8","23";"y";"7","29";"z" nL"2","0";"If ABP=z";"4","0";"and ADC=y";"6","0";" then:-" qp$(1)="y=z":p$(2)="y+z=180":p$(3)="90+y=z":a$=" AN EXTERIOR OF A CYCLIC QUAD. = THE INTERIOR OPPOSITE ANGLE ":80P "935":i=(*5)*10 +100d:"12","18";"Q";"7","29";"?";"11","22";"^";"12","22";i;"":"180","100":-9 ,-3,-/3 "2","0";"If QDC=";i;"";"4","0";" Then ";"6","0";" ABP=?":p$(1)=(180-i)+"":p$(2)=i+"":p$(3)=(i-30)+"" ^a$=" "+i+" is ext. of cyclic quad. SO ABC="+i+" AND ABP=180-"+i+"":80P N"935":i=((*4)+5)*10 :j=((*4)+3)*10 Y"3","26";"?";"7","29";i;"";"12","24";j;"->";"8","31";"P";"12","30";"Q" "2","0";"If ABP=";i;"";"4","0";"and BQC=";j;"";"7","0";" Then  DAB=?":p$(1)=(180-i-j)+"":p$(2)=(i+5)+"":p$(3)=(90Z+j)+"" ha$=" CBQ="+i+" (vert.opp.s) SO BCQ= 180-"+i+"-"+j+" THEN opp. cyclic quad. ":80P `"900":"200","171":"-80","-43":"80","-43":"181","160":"20","-32":"-20","-32" K"176","98":"2","5":"4","-2":"177","157":"1","-4":"5","2" Ҁ"5","14";"O";"1","21";"T";"10","21";"S";"2","0";"OT and OS";"4","0";"are tangents.";"7","0";" Always:- " բa$=" TANGENTS FROM AN EXTERNAL POINT ARE EQUAL IN LENGTH ":p$(1)="OT=OS":p$(2)="OT=2 x radius":p$(3)="OT+OS=2xxr":80P "980":"940":"108","26":"-108","-26":"103","-30":"5","19";"P";"2","29";"Q";"8","19";"R";"10","28";"S" B"15","0";" OP X OQ = OR X OS = OT ":"9000":ڰ"5":"5": ;"970":"940":"130","0":"201","128":"-34","-18" A"6","19";"P";"6","25";"C";"6","30";"Q";"9","20";"S" i=(*3):"2","0";"C is the centre";"4","0";"If OT=";4+4*i;"cm";"6","0";"and OP=";5+5*i-2*(i=2)-(3+3*i-4*(i=2));"cm";"8","0";"So CS=?" p$(1)=(3+3*i-4*(i=2))+"cm":p$(2)=((5+5*i-2*(i=2))-(3+3*i-4*(i=2)))+"cm":p$(3)=(4+3*i-4*(i=2))+"cm" a$=" OT=OPxOQ SO "+(4+4*i)+"="+p$(2,1)+"x("+p$(2,1)+"+2r)   SO CS=r="+p$(1,14):80P /"980":"990":"234","144":"-72","-10": `"3","4";"FOR AN";"4","1";"INTERNAL POINT";"15","1";" PN x NQ = RN x NS ":"9000" 07"970":"940":"990":"234","144":"-114","-16" 3Wi=(*4)+2:i=i+(i=5):j=(*5)+2:k=j*(j+12 /i+i) 6;ް"1":"2","26";"2";"7","25";"6";"4","28";i:ް"0" 9j"2","17";"";k;"2","0";"NQ=";i;"cm":"RN=2cm":"NS=6cm":"OT=";k;"cm";"8","0";" SO  OP=? " \,0:23613=\+1+256*23614>\,0 7:7:7::9 ;0,0;" Program loading ";0,18;1;" PLEASE WAIT ";0:0,0;:"sc":1:1:1:0,0;:"gr""p",480:0,0;:"6": tsc @           88     8?88;?88 8            @     ||@~<<~B<>?   88     8?88;?88 8   ?  B    H  B8<8h88x<B@@B@@BB           88     888;888     !       B    H  B DD TD<0DDB@|B<|BB           8?;;8   ??>;?8?  &0    2   0"   ! (  | DD ??;;8   ;8     0      ?@ 8              8  8      8|8888888                    ""  88           ?88   8|88;888        ?      $B   0  ! $B   $   $   D [     UJk5R      $T*Q$Y|     ddD!DIE""&&    / &$D"$Ad0    @D"!D"! Aa    # $@  ? >    mv      ꔫ5)Wh    ?$I)($   BI"IDB!8    |0!H  >  ?`DB!B" s    / $P    ? "@"   0!g滂      (U      !H%(I/     s!$I$A    A0B HB  '0aB!B!`@  ? x    ""   0#۵_   ?*IUUT   'ؑ"))%D     bDI"!Fc#  ?aA@!a 8 "B!BD `A  @  ? $   " !"(   ('W[       |ԒUYI+>      ;"DIII"D     ! 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BDD ~BDBx@  DT ???        ???? 8888 888888888;888          >::>>>>>>>>99>>99;;>>>>>>>>>>::88::88>>99;;99;;99;;99;;>>::88::88>>99;;9>;;99;;9>;;>55,55,",55,".gr 0 : 20HH0 @~$$BB$  6 MکA.Cowley Apr.1983 "23613"+"256"*"23614","0":"23613"+"1"+"256"*"23614","0":ٰ"9":"1":ڰ"1":"0","0";" STOP TAPE & press ENTER ":"0":"62" 6"98","126":"60","-60":"98","66":"60","60":30,-30,-:-30,-30,-:-30,-30,-:-30,30,-:-30,30,-:30,30,-:30,30,-:30,-30,-: :,"9","14";"ROSE";"10","12";"SOFTWARE" <ٰ"9":"72","24":"103","0":"72","15":"103","0":"0","11";" Hi there ";"19","9";" Geometry 6 ":"9000" >1ind="0":o$=" " ? y="0":h="0":u="0":v="0" F"2":ڰ"2"::۰"1":"0","3";"TYPICAL 'O' LEVEL QUESTIONS":۰"0":"9","0";"Don't forget there may be more than one HELP per question":"9000" d5z="4":w$="":f$="(omit 'cm')":"6":ڰ"6":ٰ"9": g"186","145":"-4","4":"4","-4":"-4","-4":"186","96":"-4","4":"4","-4":"-4","-4":"220","145":"-90","-49":"122","0":"-32","49":"-66","0":"-24","-49" jް"1":"7","22";"?";"4","19";"z";"4","27";"z";"3","18";"P";"3","28";"Q";"10","31";"R";"10","16";"S":ް"0" mmk=(*3)+"2":j=(*3)+"5":p$=(k*j):"2","22";k^2;"cm";"11","22";j^2;"cm" p"2","0";"PQ is parallel";"3","0";"to SR";"5","0";"PQ=";k^2;"cm";"6","0";"SR=";j^2;"cm";"8","0";"SPQ=SQR";"10","0";" So SQ = ? " s_"8100":w$="y"l=y+(y=0)̰"5":"7010":"797"+3*l:"9000":l:"8161":"120" v7h="1""7010":797+3*y:"9000":"115" 1w$="":z="3":f$="(omit sign)":"0":ڰ"0": N152,120x,67C*.73333:208,114r,524*.73333 S"183","85":"55","49":"5","-22":"-84","54":"26","-79":"-25","-23" }"185","87":"7","60":"0","19";"R";"2","24";"P";"4","30";"A";"8","31";"B";"12","23";"Q";"13","19";"T" \k=((*6)+19)*5:"11","17";k;"";"5","30";"?":p$=(180-k) {"0","0";"AQT is a";"2","0";"tangent to";"4","0";"circle RPQ";"6","0";"RQT=";k;"";"8","0";"So QAB=?" _"8100":w$="y"l=y+(y=0)̰"4":"7010":"821"+3*l:"9000":l:"8161":"180" 7h="1""7010":8215+3*y:"9000":"172" J"5":ڰ"5":ٰ"9"::z="2":n="0":"6","21";"?";"12","0";"QOS=?" Ak=((*3)+1)*20:p$=(180-k):700 kz="1":n="10":p$=(90Z-k/2):"12","0";"ACB=?";"10","14";"^";"11","14";"?":"700" ind="1":z="2":n="20":p$=((180-(90Z-k/2))/2):"12","0";"CQR=?";"10","19";"^";"11","19";"?":"700" "100" Y::"54":"0","14";ڰ"2";" END ":ٰ"9":"9000":"58" \w$="":162,128,30:"248","97":"-136","0":"42","78":"94","-78" D"162","128":"21","23":"-47","-9":"26","-44":"0","30" Ťް"1":"11","28";k;"";"10","29";"^";"5","19";"O";"0","18";"A";"10","31";"B";"10","13";"C";"3","16";"R";"2","23";"S";"10","20";"Q":ް"0" Y"116","102":4,-4,-/2:"142","142":-1,-6,-/2 ˙"0","0";"O is the centre":"2","0";"of the";"4","0";"inscribed";"6","0";"circle QRS";"8","0";"ABC=";k;" and";"10","0";"ACB=QRS" n"8100":w$="y"l=y+(y=0)z+1:"7010":837E+n+3*l:"9000":l:"8161":230+n 9h="1""7010":837E+n+3*y:"9000":"721"   cް"1":"15","0";" PQS=QSR ";:" (alternate angles)";"4","24";"u";"9","18";"u":ް"0": #P"15","3";"Triangles PQS and QSR are";"16","4";"similar (equal angles)": &K"15","5";"Compare the sides of the";"16","8";"similar triangles.": )"13","0";"PQ (from PQS) QS (from QSR)";"14","0";"--";"14","15";"= --";"15","0";"QS";"15","17";"SR";"17","7";" So  ";"17","13"-(k=4);k^2;" QS";"18","12";"-- = --";"19","12";"QS ";j^2: ,z"13","0";o$;"15","0";"So QS = (";k^2;" x ";j^2;")";"17","3";"QS = ";k;" x ";j;" = ";k*j;"cm": 8H"16","11";"RPQ=";k;"";"18","2";"(alternate segment theorem)": ;3"16","6";"QPB=180-";k;"=";180-k;"": >e"16","11";"QPB=QAB";"18","4";"(angles in same segment";"19","6";"subtended by arc QB)": A"16","9";"So";:" QAB=";180-k;"";"18","0";"NOTE that RQ is parallel to AB since RQA=QAB=";180-k;" (alt. s)": Hu"16","11";" OQB=90 ":"18","0";"Angle between tangent and radius":"163","102":"4","0":"0","-4": KQ"16","0";"The sum of the internal s of a quadrilateral = 360 (See OSBQ)": Ni"16","3";"QOS=360-OSB-SBQ-BQO";"18","0";"So QOS=360-90-";k;"-90=";180-k;"": R"15","10";"QOS=2xQRS":"17","0";" at centre & at circumference";"19","0";"and we know QOS from previous question": U"15","6";"QOS=180-";k;"=";180-k;"":"17","2";" So ":"17","6";"QRS = ";90Z-k/2;" = ACB ": \"15","12";"ACB=";90Z-k/2;"":"17","4";"(from previous question)";"10","14";"^";"11","14";90Z-k/2;"": _G"15","7";" CRQ is isosceles ":"17","8";"(tangents CR=CQ)": b^"17","7";"So":"17","10";"CRQ=CQR=";(180-(90Z-k/2))/2;"": b i="14"̰"21":i,"0";o$:i: "7010":y12 a$="RUBBISH" a$="h""8260" a$<"46"ůa$>"57""8106" ,"7010":"15","1";"Your answer: ";a$:0,60<:128+8*a$,0:0,-16:-128-8*a$,0:0,16:0,40(:111o,0:0,31:111o,0:17,0;"CORRECT ANSWER";:" ";p$:a$=p$8157 'װ".5","-10":װ"1.5","-20":v=v+"1" v"0","16":"207","0":"0","7":"207","0":"20","0";" Like to see why? ";:" y or n ":=""8143 !w$=:w$"y"w$"n"8146 """8149"  w$="y"  "8161" Fװ".2","2":װ".2","2":װ".2","4":װ".2","4":װ".5","9":u=u+"1"  "9000" sڰ"3"::"3","6";" TOTAL CORRECT : ";u;"6","6";" TOTAL INCORRECT: ";v:ind="0"ڰ"0":"9000":"8169" ]"64","48":"119","0":"64","39":"119","0":16,8;" More?  y or n " !q$=:q$"y"q$"n"8163 q$="n""345" 'y="0":h="0":w$="":ڰ"5":"5":: Dyz"8133" Gh="1":y=y+"1": #("""9000" #),"21","0";o$;"21","9";"Press any key" #*="""9002" #+"""9003" #. nyhuvzkjbnO A9QyWF (omit 'cm')P24