Changeset 99 in CGBLisp
- Timestamp:
- Feb 2, 2009, 9:00:58 PM (15 years ago)
- File:
-
- 1 edited
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trunk/examples/prover-apollonius.lisp
r1 r99 1 1 ;; 2 ;; Prove Apollonius circle theorem 2 ;; Prove Apollonius Circle Theorem: 3 ;;---------------------------------------------------------------- 4 ;; If ABC is a right triangle with hypotenuse BC, 5 ;; and 3 6 ;; 7 ;; 1) M is the midpoint of BC; 8 ;; 2) M1 is the midpoint of AB; 9 ;; 3) M2 is the midpoint of AC; 10 ;; 4) is the foot of the altitude dropped from A; 11 ;; 12 ;; then A, H, M1, M2 and M lie on the same circle. 13 ;;---------------------------------------------------------------- 14 ;; 15 4 16 (prove-theorem 5 ((perpendicular A B A C) 17 18 ;; If 19 ( 20 ;; AB _|_ AC 21 (perpendicular A B A C) 22 23 ;; M is the midpoint of BC 6 24 (midpoint B C M) 25 26 ;; O is the midpoint of AM 7 27 (midpoint A M O) 28 29 ;; H lies on BC 8 30 (collinear B H C) 9 (perpendicular A H B C)) 10 ((equidistant M O H O) 31 32 ;; AH _|_ BC 33 (perpendicular A H B C) 34 35 ) 36 37 ;; Then 38 39 ( 40 ;; MO = HO 41 (equidistant M O H O) 42 43 ;; or 44 45 ;; B = C 11 46 (identical-points B C) 12 )) 47 48 ) 49 )
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