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• ™™™™q8Šàs"”“†Y•Žsˆ ÊÈ#ŠæC—ep˜ª˜¶ˆ£ˆY‰R‡„Řˆ|76.2† ¢ˆ×†N †Å@  † ††ÊÈ ƒ`†E@†&Ð6–°†%p2 ™Ž†ˆYÄ@"”Y Žˆˆ †"!Ę{††• ÈÀ–~9$ 5˜†¶ • ™™™™q8Š~p9#† YˆŠˆÁˆÎÄH Š×F˜Å„†<‰AŒÅi•W@Bi¨Å!ŒÁŸˆŸ"¢ˆfr˜A‰9#‡c!Ƙ+†$´ä ™˜‡‰h ™u@!Šð—1qW€g†.‹—%†BÈÈ `D@†Ð6–°† ˆˆ ™wPŽ †&†>Å@  %†$†'†XÆ@ ’ˆ0$ Fˆx"†!††ˆ.ˆ;ˆYˆG††† ††††Ž…ˆsˆMŽ ˆˆ%ˆ!ˆ9ˆ!ˆ)ˆQˆaˆi †††† †Žç†† † ŽX‰'ˆ ‘[‰=-Gconjecture: When the angle BGH is 45 degree,Šlengthˆˆ* shortest\ŒOreplaceŠFcorner by a circleΈu(†Î†ˆ Š7g%ƒ‚h† `€ˆ•F`Š &#'Aau†4 i#i†˜DvˆŠK†r† ˆ#ˆ A† ŽkLŽ'ˆxC˜ ˆ_’ x˜yŽ †qˆq)†¾9ÉÀ  ˆÇ2@†ÎÐ6–°†ÕC˜B “ŠÄ6H‘Q‡¬ŽGˆû Length GH: ÿÿü†ž$†*‡,ÀH ŒnG˜n˜W%hG!‰¤n+ŽCƒŒCH˜±w!&I˜†m ™ ¦žG,”ø1@†Ð6–°† C˜B “† `yˆV€'† ††ŠŠ î BGH: ÿÿü†ž †0 †-†`ÈÀ  Š–i †6@"† Y™dYE(Š e$†yh†  ™†3.†B ÈÀ!¤B˜o ¡” /†BÈÈ"ƒ`†5A˜î˜×•²O0ŒC  ŠCB°C¡&– 1‡jÄ@‘ Ž˜ˆÞ2ŽŽâŽo.Š ”å3†‡•N† )"s† ™UbŒ w!&P†!ˆ —@CX`Œ$qF †:#‚#Š6$’ŠHIe•ŠHb–7$w’(h<”WŠae4g€ŒH62™dF†Ž$H0pŒxTsIŽx8 —4ŽHWG’xq’0Š – ˆôˆøŠÛŠà )3Ž\2•5Œ8)‡@ŒìDc€$’U¼†%—Ž˜rxAŽ0e2„™Ž°bpu”ÔTøpt„ø‚(t`4q$1@)!pt@5gpQ’†0@‡‘Ž ƒŠˆˆŽ4†.5ÄH  5†ÄÈ ŠFˆPÐ6–°†W9s5‘fˆ+ ™B13—G‰ŠmžU6†ƒÀˆU–BŠ“Œ£U” pwˆ&ŠZ†7†ÅȆ…`ˆÎD˜…°Cž…8œCE˜Èp”†’’Šz˜C9†C%È@—ˆ˜ˆÞ:‡%Ęˆo69€BUVcŠL“j ™P”d1W‰G6„‡¦ ˜†;”J†+†<†  ÈÀ  Š@†Ð6–°† Ž&Š’ ˜ˆ0†=†FÈÈ"ƒ ˆ[C–G`²;˜>†•Ä@‰ŽYˆŸ?†¯Ç@ ’ˆo<AîK޲œ8ˆ×-ŽßA¢V*†.†B‡Å ˆ8ˆC†t†t”ˆ6†D‡=Æ@"”5Žˆ"ˆ 9†:Ž.8†7ŽÄˆâˆÐ2†1ކ/—A–ˆŒçŒAˆIˆQŠm*†+†3†,†)†††4Ž [Š\Œ# Replace the corner by an ellipseΈ0E†4ΆOˆOŒCŠ1”˜fI† `'d•Ap0† `”7——X†o (…xUˆ†˜DvŽ˜†Ár† Ž  A† ŽkLŽ'ˆ»C˜ u˜x˜yŽ †qˆqF‡%9ÈÀ  ŠK3@‡5Ð6–°†TpW‘ŠÄR2UfˆÄЬ“:‡d î EHI: ÿÿü†ž †Ü †G†j’j–iV‰Y™—&ˆuY™ (`%h3‡†H†  ÉÈ  † @†Ð6–°†Š†)Œ*’˜ †I†KÊÈ#`†5D–C˜8'P°OJ†ŽÈÈ ƒŒCE°C¶‡K†ÑÄ@ÈŽ˜ˆÞL†ëÆ@ ’ˆoH07.2† ”åM†‡9ÈÈ"Œ*2— TpW‘† `"“X•u0©Length of HI: ÿÿü†ž­†G†N‡†ÀH ‹}H±;!&0xˆÑ†ŒO†ÀH  ˆI@† Ð6–°†'%c(hv†&ž6žEP†W9ÈÈ"ŒG1˜GTpW‘† `“U5„ˆe¢S Coord of I: ÿÿü†žg޶ˆQ†w’wˆ†'‘‘‡!ˆÊ ™ 1y‡QŠÀ ™` ˆ' ™”—ˆ·†Ý5$R0ŽIGui`Ž$d6†"ŠWy˜Xa<–b”dŽ0ph Ž$4yEuŠÙWtw6€Œl„1ˆŽ`IbpŒ„bTp@‰r‡a%$6‰k‰m&PŽx%bUŽH5€R0 &eIŠ `††`t2%PŠ SƒBŠ,ˆTCŠ8 TFpŠD‚B@ŒPdut Œ\UwˆXŒ< ”c€Žt„g$Ž€f˜ŒŒCs&gˆ—DX“eŽ`‡&c‡`Ž„YPR&ŒlXdŒl†”†Žbˆ—w¨Dt83ŽÀ6P…Œ`†ø37‚ŒTˆøR‡Ä@ ŠOˆ/O†S‡$ ÈÀˆãÐ6–°† '‰F ™™™™™™Š ˜†J†T†FÈÈ ŠÃF–G7‹h‹kž;˜U‡­Ç@ ŒîJ†S†V† Ä@  † †T†S`,u† W†*ƘO†GŽX¢<N†H†Y†bÅ ˆ8ˆZ†85ÄH"’[†ÄÈ ІG@†¢Ð6–°†‰$ƒ‚2†& 4DRDiŠ <Ž \†ÕÁÈÉ—P†Œ*ˆ ŠB!eT@ˆä ugVvŠZŠ0‡†f‡” Ž ]†^ÁH ‹'A˜¡°kž¡^‡vÉÈ `ŠCB˜C¾~C_‡¹ÊÈ#`C@†Ð6–°†!eT@T† ugVvŠ ˆ*ˆ.Ž ˆ: ÈÈ" ˆC–Bs4q i†[ Y™#“q’†  ™fIdˆJ ™†3]†7^†a†„Ä@ ŒJŽˆšb¢ˆ0`[,]1† c†¼ ÉÈ ¦‚šv’Ž ™bc…qRŽ¿Šh_†d‡Å@#š‚ˆ`e¢œˆ0c07.2† f‡&È º\†g†8'ÄH!œºˆhŠ@ ”lˆ‚ˆ‰1!š‰žcW–2g”‰f8F8Fƒ‹O† ™– 2e0b† —†j†'.È@  0k†3ÈÀ–\†[†G†l¢0ˆˆ4m¢Jˆ4ˆˆdˆ<ˆ"ˆ@ˆˆn†£1Ä 2ˆPHŽ V†U†S†L†KŽI†i†e†d†c†ˆÓa†`†h†g†fŽP]†^†_†J†Tˆmžˆ)ˆYˆ!ˆeˆ%ˆyûN†O†Q†P†M†Ff2ˆMZ“s[Š\ŽΈo† Î|Œ#Šw2–—4xŠÀbd8hu`r2–—4I† 6“sƒŠ †† ˆ v† †-†2r† Ž A† 'LŽ'ˆAC˜ ˆk’ x˜yŽ †qˆqp†–ÉÀ Žu(†-(`Ž„†§qVŠ(†³wB @Žxi10Ž$t‘“fqˆ€Ž<Ru&yPŽH4“9y0 %ƒŠs!2(ŠT ™9x—ˆ”† wQŒ”hXŠHY—tcsŠxY™'Ia‘ŠlY™ %9V‹JY™ 0i–Š„`E9†† g&ŠT`„—U’‹z`˜CW†ŠÀ`EtŽ$–V'@` qWpŽ D$f0Œ’20˜Žvd@`Œ0V€YŽ<31‡„Ž<€Ž<y5‰%ˆ`Y™ti†'Š`Y™a’6R P†R’Šl ™UVq7Œ D)fŠœ ™•VŠ$D–wŠ`D0%ŠŠŒ$†(†Ö(PVWd8` –Š”) €ŽP U7P Eˆh7E5 Ž XŠ÷ˆ€‚ƒqŠì €HŽŒ5#ޤa`f$†PF޼'(޼% (Ž4aIŽà3hPŽÔŽ„‚†€"Ž%yV@V2t`PŽ a†EŽ v q€ˆ$ ™Dv…cŒ #“iaŠ0 ™ p0ƒ4`Œ$59Š †T9A 0Ž`dA ŽlV Ž"7dŒ„B–d‘ˆ†fI!)Žœ†(`YŠxP‘@ŽTƒeŽÀ&‰‚Žlƒ4SwŠ´Gd‚‚pŽä˜`DŽlPVWdŽl†q‡2Ã@"Š£ˆr‡ÁH ƒŠµG‰(Ð6–°‡/VPˆ‡ˆ"` a%r$ˆK ™<ŽCs‡[ÂH#ŠøHšC6#tE‰5 ™p2`cŠOžCt‡žÅH–˜ˆUu‡´Àˆ" @†Ð6–°† PІY˜ ˆ%qX!‰† ˆv†9ÈÈ"ƒ`ˆBA–C°C˜O†wœCB¬C‘Šl˜Cx†C%ÈH ŽÈŽ˜u†y†ÙÄ@ ’ˆoˆz†óÆ@!”s†{‡ ÉÀ"Ž—”F)˜2r‡* Y™1%X—GŠ E@RU˜ˆF|ŒvF†ˆ7ˆv}‡iŘˆˆvˆ~†5Å@!”ȆJÄÈ ‹¢F—£V€Y@ `B–YY…† Y™††Š†€†!ÀÈ" Ša8BYf0Š*!ƒ’ˆ ˜`1P `uP ™ ” Ž!†^ÀH Š^C@†Ð6–°†°kž¡‚†ÂÈÈ!Š‚D˜C¾~CƒŒC ŽCEš†®ÙžC„‡H ÉÀ!€'–ÈVa)6aB‹]S†01d‹6ai‰‹u‰ ˆÌ‰†Ä@ qŽˆ`†Ž‹‚†„Õà† ‡† ÈÀ † @†Ð6–°†&S†01d†1 ™Va)6aBŠ ‡8UB”†H ˜†3†7ƒ†ˆ†ZÇ@ ŒJŽˆ`‰†tĘˆ0‡ u† І‚&È 8€†‹†8'š8ˆºˆŒ¢ˆ‚ˆ††!š†„ŠlW–2g”‰f˜hA—ŠÙ&†%¹ VAVAåއ7.˘W†·3‡9”ˆ†{†ˆ].šÕˆˆ4‘Œ#”ˆ4ˆˆdˆ<ˆ"ˆˆˆ’†í1•?†€†HŽ †‰†ˆ†‡†††…†„†Œ†‹†ŠŽ4x†y†u†w†v††‚†ƒ†\Žˆˆ%˜ˆAˆq{†r†s†p††”(ˆ9~Ž [Š\ŽΈ“† ÎhŒ#Š AasV™X† ` r—ƒPŠ %ƒ‚d0†C 9%“ 7†˜Dˆ±ŒKŽšŽ  A† ŽkLŽ'ˆ›C˜ ˆê’ ‰$’ ‰-‡t†qˆq”‡‚9ÈÀ  ŠK5@‡’Ð6–°†€h™IŠ ŠÅR¬“ Coord of F: ÿÿü†††Š†#†•†0ÇÈ  †9F@†@Ð6–°†)‡c!W(†& (pqUŠ žK†r–†w9ÊÀ ŒG4˜Gƒ™€ŒGB r—X¨G Length FI²µ†—†å ÈÀ#…е–´’„H)‡Y™#g„'ˆÙ ™3ƒ2€9I‡ ˜†3†ÃH#Ž÷I˜÷™*3EƒwYs†7Yˆ7˜‰:™‡nÄ@ ‹>†&ŠYˆŸš‡ˆƘ‰j—Õ*ØŽˆ"ˆ@ˆ.›ŽH‡?†˜†œ†  ËÀ! Š@†Ð6–°†" ™™™™™™†- ˆŽ5’ ŽE†NÈÈ `ˆWA–C˜(’  NžœCB°C¶†Ÿ†ÔÄ@ ŽÈŽ˜ˆÞ †îƘˆoœÕÐ0† ¡‡ ؉¢†‘ÈÀ™’„H)‹#g„'"† Y™3ƒ2€9P†BYˆBˆF£‡h9ÊÈ\3—]3™€…‹‡ r—U© î BHG: ÿÿü†‰º†ˆ †¤†ÈÀ  Š@†#Ð6–°†*#g„'ˆY™’„H)Œ ‚ƒ0FQ(ŒEœ† –Z¥†R9’R2–SI€…Š€)Q( QŽŒ–@†¥Length of HG: ÿÿü†ž'†¦†×ÀH ŠÃG–Ä`r”p†*¤e— §œCH——5VE5q5¨´ˆ¨‡a!Ä@‘M_¢W–2g”‰f€†©‡ˆŘ'•†¢††ª@1—“6I€…u r—UŠ ††Œ† Coord of G: ÿÿü†ž%†¦Ž«†UÄ@  "§†œ†¬ª¤Ž"­Ž’ˆR®†£ ÉÀ#Ž@†²Ð6–°† ˜­ ™™™™™™Š ž ž†¯†éÈÈ `†òC–G•*¢ÿ˜ˆsœ½ˆYˆŸ±‡FÆ@#”ˆoˆ‡_²‡dŘ8ˆ×ˆõˆ³†V5šVˆŽ´†¯Ȉ à õ†– –†µ†'ÀH  ˆ0D@†7Ð6–°†>°C’ Œ¶†jÆH#ŽCEšC"`uІXt&Dˆ¨C·†­%È@ І˜´†¸†ÇĘˆo´5€€™T†ä ™’ê ™– &1W‰G‡ ˜†¹†JšJ¤Ždº¢d•Žˆ"ˆ ˆ ˆŠ±†‰®† †Ÿ†œ††ž†¯Žº‰ˆ¾–ˆ)ˆ!ˆ=˜%m¦†§†ª†¢¥†£†˜†—†–†”†††³Ž [†19QNote: finding the shortest distance HG is equivalent toŠ2Š/minimum area forŽYAˆKtriangle HBG. So w†_et upŠj largrangeˆ\ation--see maple.Ž¢ªeAct020009ropes.EAC010000002204É  ropes.EAC” ACT†† ˆ*†.Š Ž Ž$]E †(Œ'%[ˆZJames Stewart (C&C)Ž page 315Ž+Refer to the journal fileŽLAC and BD are securedŽiby a ˆÉ CED.ކˆâ Objective:Ž™ Show thatŠoshortestŽ·length of suchŽZŽÔ+oc†zs when ín1=ín2. 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