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