5 2k;/ca$pmL`2rL80 xooffGGyyyy33ffff msgmxs sJ!R$F The orthic triangle is a triangle whose vertices are the feet of the three altitudes of an acute triangle. Both triangles have their own centers and when those centers are all located on one construction, their relationship is more easily seen. First, it is interesting to note that the original orthocenter H and the new Incenter I are the same point.For an equilateral triangle, all eight centers are the same point. When the original triangle is isosceles, all the points occur in a line. When the triangle becomes right, the orthic triangles sides come together to create a segment from the right vertex to the midpoint of the hypotenuse. Thus, when the triangle is obtuse, the orthic triangle cannot exist. The orthocenter exits the triangle when the angle is obtuse, but the Incenter must stay within the sides. Because these type of centers are shared in the orthic triangle, the triangle is bounded to have an acute parent. When the original triangle is equilateral, the orthic triangle closely resembles the medial triangle in that they are both one fourth the original area.BA@BA@B@BAAA@BAAAA@BAAAAA@BA(o8!`80 xooHHo)o80o9oThe Orthic Triangleo82o)o8@o]Po8Po]Po7o8po]P 80 xooAd7C4  c1|Cs@ MOC\ 80 xooB7C<7Cl 7XZ6  |D"Cg  ; 80 xooCEDBdA.@!K?HP 7Cl 7C,l 7C|D+4   80 xoop3p1oppo|??D+4D"CgCs@9H 80 xoom3|  m{!:A}BAC = 2<J|F0||`5÷F01lF0HuPF06)FF0|`HuPP6||`||`#L  ||HuPF6#FHuP| HuVHuP|7 Angle(BAC) = | |HuP6#LHuP||HuP6#,HuP||`@|7$# HuP|;+HuP)Jp#|2|#z1l|||`|aB#o2:XopÑPF#o7#p8F o800"9:X :Xoo9nroofoonGSP! :X9"H`8tݐHuP8l#LHuP||HuP8#,HuP|$3 80 xoom2|  m{!:A}CBA = 2<J|F0||`5÷F01lF0HuPF06)FF0|`HuPP6||`||`#L  ||HuPF6#FHuP| HuVHuP|7 Angle(CBA) = | |HuP6#LHuP||HuP6#,HuP||`@|7$# HuP|;+HuP)Jp#|2|#z1l|||`|aB#o2:XopÑPF#o7#p8F o800"9:X :Xoo9nroofoonGSP! :X9"H`8tݐHuP8l#LHuP||HuP8#,HuP| 80 xoom1|  m{!:A}ACB = 2<J|F0||`5÷F01lF0HuPF06)FF0|`HuPP6||`||`#L  ||HuPF6#FHuP| HuVHuP|7 Angle(ACB) = | |HuP6#LHuP||HuP6#,HuP||`@|7$# HuP|;+HuP)Jp#|2|#z1l|||`|aB#o2:XopÑPF#o7#p8F o800"9:X :Xoo9nroofoonGSP! :X9"H`8tݐHuP8l#LHuP||HuP8#,HuP|  80 xoojnCCCA0AXZ?PH7Cd7C4d7C|D"CgCs@?  80 xookt 7C   a4|Cs@D+4?7L  80 xoolI:D Ilh7C7C7CL7C7C7C7C|D+4D"Cg?k?I  80 xooq'(z~z~#oC:\WIN98\EXPLO|D"CgDYC ?'  80 xoorp5 c1'|Cs@CZAY?Nap 80 xoom4ppp| Area ABC = 2<J|F0||`5÷F01lF0HuPF06)FF0|`HuPP6||`||`#L  ||HuPF6#FHuP| HuVHuP|7Area(Polygon ABC) = |HuP6#LHuP||HuP6#,HuP||`@|7$# HuP|;+HuP)Jp#|2|#z1l|||`|aB#o2:XopÑPF#o7#p8F o800"9:X :Xoo9nroofoonGSP! :X9"H`8tݐHuP8l#LHuP||HuP8#,HuP|'a 80 xooaf|D CDGx? ' 80 xoon G'|CAB`? '  80 xoooI?CmC L D7CD7C7CD7C!|D`AD(C@? D7I< 80 xooI '?'? wּw|D9B ty 80 xooGhh|C@B  80 xooHP @ |C@ [` 80 xooI A|D'B .3 80 xooV|D C4E  joIF M 80 xooU(_[|~|~|D  :? 80 xooTMMUNICATOR\PROGRAM\NETSCAPE.EXE|D(Bo1 5t:y 80 xooH h'?'? wVw|DBZ* 4' 80 xootI7E<J B|CCD ¬? ~'( 80 xoov9CC pI|CrCCI? `d  80 xooxd_Text.charAt(; |Cs@D'B?  80 xooy=nl,DC  xIIf|D"CgC@?0p  80 xoop2oooooopppppppppppp|?pD(Bo1DD C4E?  80 xooak|D(Bo1DnBS?i'  80 xooaj|DD}BGz?i?  80 xooai|D(Bo1D?9-  80 xooah|D C4ED(Bo1?-o  80 xooag|DD C4E?BG 80 xooC h'?'? wVw|C!'Buy = B  80 xooG'?'? wּw|DUB}UU ex 80 xoom5| Area VUT = 2<J|F0||`5÷F01lF0HuPF06)FF0|`HuPP6||`||`#L  ||HuPF6#FHuP| HuVHuP|7Area(Polygon VUT) = |HuP6#LHuP||HuP6#,HuP||`@|7$# HuP|;+HuP)Jp#|2|#z1l|||`|aB#o2:XopÑPF#o7#p8F o800"9:X :Xoo9nroofoonGSP! :X9"H`8tݐHuP8l#LHuP||HuP8#,HuP|  80 xooAAM{:4M|D!A2  "FLKQ@ 80 xooZ@@@@@@@@|DNBP $vf{k 80 xooY)zDlj ZP&l |D ;BQ #' 80 xooao|CgCND:4CВ?"M!' 80 xooal|D » D*,NA1@@< `#5t:y 80 xooI'ƣwե2 $t _$t |DBZ*! o  80 xoom6-$4 fbQ 8-F| !{D:{(:Area ABC}}{{(:Area VUT}} = |`5÷F01lF0HuPF06)FF0|`HuPP6||`||`#L  ||HuPF6#FHuP| HuVHuP|7&Area(Polygon ABC)/Area(Polygon VUT) = 6#LHuP||HuP6#,HuP||`@|7$# HuP|;+HuP)Jp#|2|#z1l|||`|aB#o2:XopÑPF#o7#p8F o800"9:X :Xoo9nroofoonGSP! :X9"H`8tݐHuP8l#LHuP||HuP8#,HuP|'e{o  80 xooau|D ;BQD?*-  80 xooat  ar|D C4ED!A2 ?("' 80 xooas|D BD)%C0?#*2' 80 xooap|D[TBD-n?"(OT 80 xooH''?'?p  w:|D:B: +,BhGm 80 xooG' D9Mll lll:t2|DbBe /0;&@+ 80 xooC'h'?'?p  w:|D Bt 12