25.3 Ceva Theorem 709
Appendix
We give those values ofλ,μ,νwith numerators and denominators< 10
for which the area of trianglePQRisktimes that ofABCwith the
numerator and denominator ofkless than 10.
λμνk λμνk λμνk λμνk
1
9
4
5
9
8
1
9
1
8
1
3
8
5
1
7
1
8
3
8
1
2
1
3
1
8
9
5
4
9
1
1 9
71 13 61 21 17 25 76 16 17 1 41 41 16 17 13 12
61 15 56 92 16 12 34 15 16 78 76 91 61 1 23 18
6
7
5
2
7
1
6
1
5
6
7
1
2
1
6
1
5
6
5
1
6
2
9
1
4
1
7 1
1
1 4
42 14 41 73 14 13 43 18 14 58 52 92 41 1 47 19
71 16 57 61 31 61 17 12 31 21 53 61 13 87 38 19
3
4
3
1
4
1
8
1
3
8
5
1
8
1
7
3
8
1
3
8
7
1
9
3
8
1
2
1
8
1
3 3
84 56 21 91 52 41 58 29 52 67 71 61 37 23 12 18
9
1
8
9
5
1
9
1
2
1
8
3
8
1
3
1
2
1
5
6
7
1
6
1
2
3
8
5
6
1
1 9
25 37 32 81 21 21 12 17 21 53 31 61 12 34 16 15
95 8 94 19 74 41 1 91 35 13 12 61 58 52 14 29
8 38
1
7
2
3
1
6 1
1
8
2
3
1
2
3
7
1
8
5
7 6
7
2
1
3 6
45 16 21 15 43 3418 45 98 19 91 56 21 38 19
67 5629 67 16 78 19 67 12 15 61 67 25 7 16
8
6
7
1
6
1
9
7
8 3
8
3
1
9
8
9
5
4 9
1
9 1
1
4
1
7
1
4(^14714191231618147419163218)
(^1741498194519873813198767619)
7
6
1
7
2
5
1
6
7
6
8
7 6
1
9
7
6 52
1
6
6
5
1
6
1
5
2
6 9
57 83 2 19 45 9 98 19 43 14 31 18 34 2615
5
2
7
1
6
1
6
3
2 16
1
8
3
2
7
3 2
1
8
8
5
1
8
1
3
1
8 7
5 4 52 29 53 2316 74 1419 95 49 18 19
(^2765162658319232731822217)
(^2838132353162643159459819)
(^7323218528542952767168378319)
(^83265198382133532163837819)
(^343418376123858177257616)
(^434318417144741194528529)
(^44437527616565629656529)
(^676871964321563211863712)
(^672571676752167411476312)
(^85831782831389459199895419)