GSPk F5c"apmGd(tIqUCTDCTDC LNDCLǷCC `2 DCsZDBefore clicking on the Hint Button below, first try to drag and resize the (Green) Circle of Inversion to make the geometry of the whole Inverted Image as simple as possible.t+   `H}D@DD@DOtDD<_X2DCX2D.D_1`ED@DdxThe problem here is to find the radii and (x, y) coordinates of their centres with respect to a stated origin (Here taken as the centre of the Circle of Inversion) of the cirlcles inside the outer arch and the semicircle. One of the easiest methods is to use Inversion Theory. See the associated Word File: D - Inversion Example 3 Notes.doc for a detailed explanation.t<5}I   y (n = 3) = t; |!   x (n = 3) = t;}   r (n = 3) = t:L Next Circle (n = 3)t:{   y (n = 2) = t9zz   x (n = 2) = t9Q{e   r (n = 2) = t84HL Next Circle (n = 2)t8y"   y (n = 1) = t7x   x (n = 1) = t7y   r (n = 1) = t6L Next Circle (n = 1)t5xv   y (n = 0) = t4Pud   x (n = 0) = t4'v;   r (n = 0) = t3 L Top Circle (n = 0)t?DLW Dn@C[,}lwDC/C@wDrCC tINVD-3DC Lµ>DCHO?DC wDM7RB#DCwDO9CC tINC_U?DbCbp?lDfCى?q<DqCaB$? DCC t?DTD@Ch}˷>DixChO>DCg! >WDCfCC twY|^BC<@D"C;L @DiC;@.D_C:@DD tY^A[sF>DCD| ?wDcCCI?D,#CBCD t %Hide Random (x,y)>M:EN䀀mR((R (4 t,Show Random (x,y)>XL:EN䀀mR((R c tK ^Move U->A t7 JMove T->B t# 6Move U->V t "Move T->W t;d^@Drag and ResizeR(>XL:EN䀀mR((R cCCW|CZ?!tz1c3CDUCF%5?F%5?tO1I@c2@DDUCF%5?F%5? tX|^meKj 666 6 d(CD@DD?t|jQxt C m6947c$7cOtOHtlL`W" Radius Drag and Resize = !Radius(Circle Drag and Resize) = t'F[ m57O\Oy~H+ HD O: Radius Drag and Resize = !Radius(Circle Drag and Resize) = tF[ m45 Radius Drag and Resize = !Radius(Circle Drag and Resize) = t$ m33 Radius Drag and Resize = !Radius(Circle Drag and Resize) = tav m30 Radius Drag and Resize = !Radius(Circle Drag and Resize) = t Y^ G CYCFPG[ G[_P G[ nDD "tqECircle of Inversion (Hint)XL:EN䀀mR((R c tTRandom Circle of InversionXL:EN䀀mR((R c t0dE m24 Radius Drag and Resize = !Radius(Circle Drag and Resize) = td m21 Radius Drag and Resize = !Radius(Circle Drag and Resize) = td m18 Radius Drag and Resize = !Radius(Circle Drag and Resize) = t4dID# m15 L;ECHOחEC w~h;D#DCwDmW˻D Radius Drag and Resize = !Radius(Circle Drag and Resize) = tY^> X_PlPA)RL DUFCD "t`<xTOP\ a= NDOWS\DESKTOP\SKETCH~1\INVERa\New_A.gsp m {S:AB} = a =  "t  EDDC ! t >kh G[_PPG[D@CD`1D?"(tzI@c1DDBF%5?F%5?(ts" ?a m59  {D:a}{{(:2 + {(:3 + 2}{u:2}}} = a/(2 + (3 + 2)^2) =  0trI!p ?a m53mart 1215 series  {D:a}{{(:2 + {(:2 + 2}{u:2}}} = a/(2 + (2 + 2)^2) =  0tq  ?a m41  {D:a}{{(:2 + {(:1 + 2}{u:2}}} = a/(2 + (1 + 2)^2) =  0tnEx ?a m26  {D:a}{{(:2 + {(:0 + 2}{u:2}}} = a/(2 + (0 + 2)^2) =  0t3h m14G[ryC#DCG[ryCCCL G[`DCG[`TX = Distance(T to X) = / t>IY#DrCwDB#DCG7%DǼC,}8LCCFCD?/t  DD@C 23t|,lS?a m67  82{!:*}{(:3 + 2}{!:*}{(:{D:a}{{(:2 + {(:3 + 2}{u:2}}}} = 2*(3 + 2)*(a/(2 + (3 + 2)^2)) =  4t|@+?a m66  *3{!:*}{(:{D:a}{{(:2 + {(:3 + 2}{u:2}}}} = 3*(a/(2 + (3 + 2)^2)) = 4tzjP?a m55  82{!:*}{(:2 + 2}{!:*}{(:{D:a}{{(:2 + {(:2 + 2}{u:2}}}} = 2*(2 + 2)*(a/(2 + (2 + 2)^2)) =  5tzq>?a m54  *3{!:*}{(:{D:a}{{(:2 + {(:2 + 2}{u:2}}}} = 3*(a/(2 + (2 + 2)^2)) = 5tyi+?a m43  82{!:*}{(:1 + 2}{!:*}{(:{D:a}{{(:2 + {(:1 + 2}{u:2}}}} = 2*(1 + 2)*(a/(2 + (1 + 2)^2)) =  6ty=(?a m42  *3{!:*}{(:{D:a}{{(:2 + {(:1 + 2}{u:2}}}} = 3*(a/(2 + (1 + 2)^2)) = 6tuoe ?a m28  82{!:*}{(:0 + 2}{!:*}{(:{D:a}{{(:2 + {(:0 + 2}{u:2}}}} = 2*(0 + 2)*(a/(2 + (0 + 2)^2)) =  7ttG8n?a m27  *3{!:*}{(:{D:a}{{(:2 + {(:0 + 2}{u:2}}}} = 3*(a/(2 + (0 + 2)^2)) = 7tJEq0 ?a m16 "{D:{(:Radius {!:C}TU}{u:2}}{TX} = 'Radius(Circle TU)^2/Distance(T to X) = .8tz[ a1DDB@#(@DDCD: t\>|^l[ @DDD@C?: t>^mCDD@C?:tY^+B'C<@D"C;L @DiC;@.D_C:*$DD <tW\+T'@Ch}˷>DixChO>DCg! >WDCfTUCC <tY^+B'C<@D"C;L @DiC;@.D_C: 'DD >tY^+B'C<@D"C;L @DiC;@.D_C:,DD @tY^+B'C<@D"C;L @DiC;@.D_C:8DD Bt+T'@Ch}˷>DixChO>DCg! >WDCfKoCC Ct Fq1Cq1C E!t9> GHDq1C F tN?!ZphC?C DtaCtc30DCu?sCCphC?C?Ot[@ a2@DDUCس]DDCCDM1tz[ > a3CDTCճ]?@DDDDCN1t_Yd^+DWz AX)DC T%Dr!Cl TA[TB%DCTApL"DUUDD "PtrYw^ AV2Cl T.HOf4DNC MLA-DfCtLiDD "QtTYY^( S AR$ [NZTP7c(hT7c_Pp7c`DD "Rt=YB^  AN2<p @ X@@ X@/DD "St Y^ AH  7DD "Tt YCsD 9UtEX` m19 "{D:{(:Radius {!:C}TU}{u:2}}{TZ} = 'Radius(Circle TU)^2/Distance(T to Z) = -Vt -b?!ABKPCD Xt>Ct8?!ADNDwC Yt >v D@CD`1D?"^tY^+AH'  7 'DD ^AtY^+AX')DC T%Dr!Cl TA[TB%DCTApL"D8,DD Z;t^>dDladC =DCrDpD TtLG[=DCئ1D)DPLTUD@CTUD`1D?"ZtY^+AV'2Cl T.HOf4DNC MLA-DfCtLL0DD [;t^RdY_ac_#5DqCH|_#@D0CHhD@ChD`1D?"[tS>YPaaooo____￿￿ 0000PP`D@C`D`1D?"\tY^+AR'$ [NZTP7c(hT7c_Pp7c -DD \=t<>By0D@C0D`1D?"]tc202}{u:2}}}}/DD]BF%5?F%5?]JtY^+AN'2<p @ X@@ X@,DD ]?'tu@(?Y_("/98CLU_t+T'@Ch}˷>DixChO>DCg! >WDCfoCC `t m20TAB = Distance(T to AB) = a t> tCCKPCD?at/ m23PR@ P@PPTAD = Distance(T to AD) = b t>u 7 FCCNDwC?btc15P W_PtW1"sRDDCF%5?F%5?^dt c31@zDPwZUUDDǝBF%5?F%5?Zet% c281"sR2LUD1CtLL6HOe['iDDǝBF%5?F%5?[gtc241"sR2 p`DDXUBF%5?F%5?\jt=Blar  AO0DhC kltSLc11CChBF%5?F%5?otE ` m22 #{D:{(:Radius {!:C}TU}{u:2}}{TAB} = (Radius(Circle TU)^2/Distance(T to AB) = ,ptFEm` m25  #{D:{(:Radius {!:C}TU}{u:2}}{TAD} = (Radius(Circle TU)^2/Distance(T to AD) = +rt  AIDC ctt_ d=D AY T&P:B=DCLOHB'C=DC L"Pb-B=TUDD futTY` ASooooo```߯???oooo`D*C iwtPU+AO'vDhC x6t AACC Wyt+T'@Ch}˷>DixChO>DCg! >WDCfdCC zt+T'@Ch}˷>DixChO>DCg! >WDCfCC {t05+AI' DC |7tg l+AY' T&P:B=DCLOHB'C=DC L"Pb-B=8NDD }4t_d+AS'ooooo```߯???ooooUUD*C ~5t,Sc211"sR20DhCAF%5?F%5?x'tuC(?AA(DOVW`oyt${c12CCʼ*CF%5?F%5?tx'c13CCLBF%5?F%5?t3c161"sR2WDCBF%5?F%5?|tYjc321"sR2C!,C)DC TUDDr@F%5?F%5?}tJb c251"sR2```D*C@U=AF%5?F%5?~t:?F AP?s[Ts [D{C t ACCWD qt AE JVsgCC stv[ AL\_C$C tgl #X AZC `K)DCpd"DC/7c)DC6+D C7c#D<D tUZ AT___,P07cwZ7cDDFC tD Show Next Object Circle>XL:EN䀀mR((R c  6@? xtcvHide___???_?0000 __φxt/ m44TAP = Distance(T to AP) =  t>z$s[ (CCD{C?'tD(?AC(Xapqz'tu(?AE JVs(Ybrs{t Hide  AB7|t@ Show Top Object Circle>XL:EN䀀mR((R c  AB7|tKQ` m32TAL = Distance(T to AL) =  t>xCC\_C$C?tR Show Next Inverted ImageXL:EN䀀mR((R c  };<4t|Tic m68| Hide ext Object Circle>XL:EN䀀mTAZ = Distance(T to AZ) =  t>ae {(:3 + 2}{u:2}}}e'F Tm6DCL";DC LK9DCTCC#D<D?tCEV Show Next Circle Objectjp Rq ^Qtt n C ~=>5 ti m56?ooooooo```o`0000ooTAT = Distance(T to AT) =  t>ab ϰ????@@@?@ppp???p ? CCDDFC?tFmmt` m46 #{D:{(:Radius {!:C}TU}{u:2}}{TAP} = (Radius(Circle TU)^2/Distance(T to AP) = %tm6x` m34  #{D:{(:Radius {!:C}TU}{u:2}}{TAL} = (Radius(Circle TU)^2/Distance(T to AL) = &te5@` m70 #{D:{(:Radius {!:C}TU}{u:2}}{TAZ} = (Radius(Circle TU)^2/Distance(T to AZ) = #t'Fm` m58 #{D:{(:Radius {!:C}TU}{u:2}}{TAT} = (Radius(Circle TU)^2/Distance(T to AT) = $t+T'@Ch}˷>DixChO>DCg! >WDCfXCC t+T'@Ch}˷>DixChO>DCg! >WDCf CC t+T'@Ch}˷>DixChO>DCg! >WDCfCC t+T'@Ch}˷>DixChO>DCg! >WDCfHCC tw(c22CC|cBF%5?F%5?tTKc18CCdBF%5?F%5?tc33C 1DCJCC TtLG[1DCe DgCPLCChBF%5?F%5?tc26 JtO O'T,CC$BF%5?F%5?t AQVCONC t AMXCoC tJ BA$C7ci,T4ThLL0 Wa$`jCӊC t AU K JV^C:C 't(?AQ('t(?AM('t~(?BA$C7ci,T4ThLL0 Wa$`(t= Hide Next Object Circle>XL:EN䀀mR((R c ; Ctx ?@6t ShowThLL0JLF T}  CLx ?@6't(?AU K JV(t%H8Hide Next Inverted CircleXL:EN䀀mR((R c p??p tO$Show Next Inverted CircleXL:EN䀀mR((R c tDHide Inverted Top CircleXL:EN䀀mR((R c tKShow Inverted Top CircleXL:EN䀀mR((R c 'V't9 Hide Top Object Circle>XL:EN䀀mR((R c  |7BAt Show  |7BAtKHide Next Inverted Imagep Rq ^Qt DBCtRShow Next Inverted Imagep Rq ^QtH DFtK Hide Next Inverted ImageXL:EN䀀mR((R c  4<;}tW>j Hide Next Circle Objectjp Rq ^Qt  5>=~tKHide Next Inverted Image  3n/O `T7ctkR~Show Next Inverted ImageXL:EN䀀mR((R c J = "Arial