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| View Original: | Fermat Point Scope.svg (286x688) | |||
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| Keywords: Fermat Point Scope.svg en A purely geometric treatment of the Fermat point own MRFS 2008-08-31 fermat proof png Source The main reason for this diagram is to emphasise that the Fermat point is NOT the same as the first isogonic center which is unfortunately a very widespread misconception The source is licensed under the same license as the image Feel free to edit fix or improve it fermat_point_scope euk <pre> Combination of 3 figures in 1 box 0 0 10 24 draw segment point 0 9 point 10 9 draw segment point 0 16 point 10 16 Proof that the Fermat point lies within the triangle A point 7 21 B point 1 18 C point 9 18 D point 4 17 E point 7 5 23 thickness 2 draw line B C draw line A B draw line A C thickness 0 5 draw segment D A draw segment D B draw segment D C draw segment E A draw segment E B draw segment E C label A 0 2 170 label B 0 2 110 label C 0 2 45 draw P' intersection line A D line B C 0 1 280 draw P D 0 1 270 draw \textbf A-zone only D 2 350 draw P' A 0 2 355 draw P E 0 2 0 draw \textbf B-zone and C-zone E 0 4 90 draw \textbf C-zone only segment A B 2 120 Case 1 - an angle at least 120 degrees H point 6 11 5 I point 1 10 J point 9 10 K point 4 8 10 5 I H F equilateral K H G equilateral thickness 2 draw H I J thickness 0 5 draw H K G draw segment F H draw segment F I draw segment F G draw segment K I draw segment K J draw A H 0 2 20 draw B I 0 2 180 draw C J 0 2 0 draw P K 0 1 270 draw Q G 0 1 210 draw F F 0 2 180 draw \textbf \Huge Case 1 F 4 5 0 mark segment K I simple 0 7 mark segment G F simple 0 7 mark segment H K double 0 7 mark segment K G double 0 7 mark segment G H double 0 7 mark segment H I triple 0 7 mark segment I F triple 0 7 mark segment F H triple 0 7 Case 2 - no angle greater than 120 degrees L point 4 8 M point 3 5 5 N point 9 5 P point 6 2 6 1 M L O equilateral N P Q equilateral N M R equilateral S intersection line N O line L R N S T equilateral thickness 2 draw L M N thickness 0 5 draw N P Q draw segment M R draw segment N R draw segment O L draw segment O M draw segment R Q draw segment P L draw segment P N draw segment M P draw segment S M draw A L 0 2 20 draw B M 0 2 180 draw C N 0 2 0 draw P P 0 2 180 draw Q Q 0 1 180 draw F O 0 2 180 draw D R 0 2 0 draw P_0 S 0 1 45 draw Q_0 T 0 1 0 draw \textbf \Huge Case 2 L 2 5 0 draw segment L R draw segment N O draw segment N T mark segment M P simple 0 7 mark segment Q R simple 0 7 mark segment N P triple 0 7 mark segment N Q triple 0 7 mark segment P Q triple 0 7 mark segment M N double 0 7 mark segment M R double 0 7 mark segment N R double 0 7 </pre> Fermat point | ||||
