o -?1GcapmM6MϺ  ! 2Draw triangle A'B'C' Scroll down . . . eventuallyg2Jg g/ _#/NnNbSD@LN^NtLOCATENENVBUO n/0<=_ JgUOHm +r! !RRR<9 K&j Take any triangle ABC. Construct equilateral triangles externally on each side and locate the center of each equilateral triangle. Label these centers A', B', and C' for the triangle centers opposite angles A, B, and C. Construct lines AA', BB', and CC'. Observe. Are they concurrent? Is the point of concurrency any of the orthocenter, centroid, incenter, or circumcenter of triangle ABC? If not, what can you find out about this point?point. this point.!$!$qѸ(qѸGZL_!Apr'`r@ lr0@r @@r'` 8r'`0CʔCzly o!Bpr'`r@ lr0@r @@r'` 8r'`0C"Cpu#p!Cpr'`r@ lr0@r @@r'` 8r'`0CC !YHHl @TYCC܀ @ZE_!Apr'`r@ lr0@r @@r'` 8r'`0C!DPj @!Bpr'`r@ lr0@r @@r'` 8r'`0C2D`@ ?D!Cpr'`r@ lr0@r @@r'` 8r'`0CD`  ()! !B8rH4%HH! >%;Th point of concurrency is the first Napoleon Point of ABC. qѸquittingclosingdqѸ] (qѸr50r5,`R9W> !AU`r@ lr0@r @@r'` 8r'`0BlDU OT$ !AVU$FU$RC܀DT@ F_Are  !js the point of concurrency any o the orthocenter, centroid, incenter, oiCʔCzC"C?uH  !k,QIhC"CCC?FYu  !lrHrUUUUIHHTCCCʔCz?? !Apr'`r@ lr0@r @@r'` 8r'`0C{^C2I rw? !Cpr'`r@ lr0@r @@r'` 8r'`0CCL ? !Apr'`r@ lr0@r @@r'` 8r'`0CCcr uz ? !Bpr'`r@ lr0@r @@r'` 8r'`0CտD '$ !akU$YHU$YpC"CCyXCþ?F'_H !alr+@YY|CʔCzC Cȟ??_Are  !js the point of concurrency any o the orthocenter, centroid, incenter, oiC!DPjC2D`@?~DH  !k,QIhC2D`@CD`? ?>_  !lrHrUUUUIHHTCD`C!DPj? w|? !Cpr'`r@ lr0@r @@r'` 8r'`0C,=D^\ ? !Bpr'`r@ lr0@r @@r'` 8r'`0CxLDU  ' !br!@`JhX|BlDUC܀DT@? FYw? !lrHrUUUUIHHTCCLCʔCz?qor !uU,GHHrCCCCL?? !j the point of concurrency any o the orthocenter, centroid, incenter, oiCCcrC"C? L_$ !xU$Rd @UxHjCʔCzCCcr?zu? !k,QIhCտDCC?z  !aaG rrr#r UUUUGLC"CCտD?ejXD!AAYtXhdYXCeJC}J 8= L!IC(:Cʩ   X!AB @Y X`ZCC@ !AC LC~ʔC=J >'a!amYplHCµDrC=JC? p'W!anYTC C`*CCz??Y|? !lrHrUUUUIHHTC,=D^\C!DPj?v>r !uU,GHHrCD`C,=D^\? D? !k,QIhCxLDUCD`? ~ !aaG rrr#r UUUUGLC2D`@CxLDU? X!AB @Y X`ZCyD`` _d !AC LCDXUa h'~!amYplHCUCDbJ?K !AnimateUDHU ee\a!LHHr#HRCsC!p !MIlL @HG0jC C$& PU!OrUGXQCLC !PUDU CyC- :!?$!RU$F @UxG jCDtD !SrrUUUUFHHCSտDD !u !aopYX<+tr+xr+rUC~ʔC=JCC?%F_unde !apt plot free points. If you plotfixed points, they will only appear oncoCʔCzCC@?$!' !aqYPcant be pasteeC@C@CD ?$'enu) !aro be missing from your Script Tol Folder. Please try again in a few mieC'CCCE(C? %X]!HHHr+\7GnsZ;CXCj '&\oat!LHHr#HRCDWc (|bg!MIlL @HG0jCD_nH ) $!RU$F @UxG jChDo *!SrrUUUUFHHCUQ&Do +^D !aopYX<+tr+xr+rUCDXUaCD`? -?_unde !apt plot free points. If you plotfixed points, they will only appear oncoC!DPjCyD``?,'I !aqYPcant be pasteeCzDNCyDr@?,;'Penu) !aro be missing from your Script Tol Folder. Please try again in a few mieCf4DmCgwpDC ?-Y^!HHHr+\7GnsZ;CDr0 /."S !ShowU$HU$Q 0$Q !Hide$HU$Q 0FY? !vrHrUUUUIHHTCʔCzC C$&?2[oGT !w,UUUUGlCDCC3CTCsC!pCC?1 !yrUL(GHC"CCyC-?4FU_ !zCLCCʔCz?3uU !abU$HU$GCCCSտDD?6!?U !acQGFrCDtDC"C?5#(!GFABFG@AGH?@HI>?IJ=>JK<=KCC1 87 !CM;<LM<=KL=>JK>?IJ?@HI@AGCC 9:?Yg? !vrHrUUUUIHHTC!DPjCD_nH?=[>tGT !w,UUUUGlCDCC3CTCDWcCD`? <DU !abU$HU$GCD`CUQ&Do?? ~ U !acQGFrChDoC2D`@?>jo!GFABFG@AGH?@HI>?IJ=>JK<=KC5D[A A@<A!CM;<LM<=KL=>JK>?IJ?@HI@AGCyDO} BCG!B'pr'`r@ lr0@r @@r'` 8r'`0CLC@ GHMR!C'pr'`r@ lr0@r @@r'` 8r'`0C\m@Cs IJ !A'pr'`r@ lr0@r @@r'` 8r'`0CG@CE KL]  !asVCCCXCj?;N ' !atH[0 @xZjCCCXCj?;Nh_mdG!B'pr'`r@ lr0@r @@r'` 8r'`0CDZm OP!A'pr'`r@ lr0@r @@r'` 8r'`0Cy6Dj QRL' !atH[0 @xZjCyDO}CDr0?DTL'$ !boU$FU$FC5D[ACDr0?DS T' !bssHG$U$ C܀DT@C5D[A?S '!ad Db zl@xQjCʔCzCG@CE?W@ '_!ae _r$FC"CCLC@?U{'!afHFkrCCC\m@Cs?V`!Show C'r'`r@ lr0@r @@r'` 8r'`0 VZ!Hide C'r'`r@ lr0@r @@r'` 8r'`0 V!Show B'r'`r@ lr0@r @@r'` 8r'`0  _U!Hide B'r'`r@ lr0@r @@r'` 8r'`0  _U;!Show A'r'`r@ lr0@r @@r'` 8r'`0  !W 1!Hide A'r'`r@ lr0@r @@r'` 8r'`0 !W =ߛ''!ad Db zl@xQjC!DPjCy6Dj?[d'_!ae _r$FC2D`@CDZm?Z! Show Lines`r@ lr0@r @@r'` 8r'`0 a`_! Hide Lines`r@ lr0@r @@r'` 8r'`0 a`_6;Y!N(1)pr'`r@ lrN{l:1}r6 @@r'` 8r'`0CCˋ `_n.s3Y!N(1)pr'`r@ lrN{l:1}r6 @@r'` 8r'`0C6JD\ 2ih't !bpU$U$RCDr0C6JD\ 2?mD'Cz !bq]C"CDCeJC½J@BD rCJCCC"CHE(CXPC6JD\ 2BlDU? m