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294 Theorem. Let A1A2A3A4A5 be a pentagram with pentagon B1B2B3B4B5 as shown in the following gure. Let Ck be the intersection of the line AkBk with the side Bk+2Bk+3, k =1,2,3,4,5. Then and B3C1 C1B4 A4 B4C2 C2B5 Proof. Lemma 2 yields B5C3 C3B1 A1 B1C4 C4B2 A5 B3 B4 C1 B3C1 C1B4 B5C3 C3B1 B2 B4C2 C2B5 B1C4 C4B2 B1 = B1A4 B5B1 = B3A1 B2B3 B5 B2C5 C5B3 A2 A3 B2B3 ; A4B2 B4B5 : A1B4 = 1 : By Menelaus's Theorem in triangle A4B5C5, wehave A4B1 B1B5 and in triangle A1B5C5, wehave A1B4 B4B5 B5A5 A5C5 B5A5 A5C5 C5B2 B2A4 C5B3 B3A1 = ,1; = ,1:
It follows that B3C1 C1B4 = B1A4 B5B1 = B1A4 B5B1 = A5C5 B5A5 = 1 : B4C2 C2B5 B2B3 A4B2 B2C5 A4B2 B5A5 A5C5 B5C3 C3B1 B3A1 B2B3 B3A1 A1B4 B1C4 C4B2 B4B5 A1B4 B4B5 C5B3 B2C5 C5B3 B2C5 C5B3 295 This result may be something already well known, but I presume the fact that its discovery has been made by a junior high school student is signi cant. Have you heard about ATOM? ATOM is \A Taste Of Mathematics" (Aime{T{On les Mathematiques). The ATOM series The booklets in the series, ATaste of Mathematics, are published by the Canadian Mathematical Society (CMS). Theyare designed as enrichment materials for high school students with an interest in and aptitude for mathematics. Some booklets in the series will also cover the materials useful for mathematical competitions at national and international levels. La collection ATOM Publies par la Societe mathematique du Canada (SMC), les livretsdela collection Aime-t-on les mathematiques (ATOM) sont destines au perfectionnement des etudiants ducycle secondaire qui manifestent un inter^et et des aptitudes pour les mathematiques. Certains livrets delacollection ATOM servent egalement de materiel de preparation aux concours de mathematiques sur l'echiquier national et international. This volume contains the problems and solutions from the 1995{1996 Mathematical Olympiads' Correspondence Program. This program has several purposes. It provides students with practice at solving and writing up solutions to Olympiad-level problems, it helps to prepare student for the Canadian Mathematical Olympiad and it is a partial criterion for the selection of the Canadian IMO team. For more information, contact the Canadian Mathematical Society.
Page 1 and 2: THE ACADEMY CORNER No. 20 Bruce Sha
Page 3 and 4: 259 8. Let k be the smallest positi
Page 5 and 6: THE OLYMPIAD CORNER No. 191 R.E. Wo
Page 7 and 8: Part II 1 p.m. - 4 p.m. 263 4. A co
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Page 11 and 12: Since 1 1 1 1 = + + + 2 2 3 5 +:::
Page 13 and 14: . . Hence 1+ 1 3 +:::+ 1 2k,1 > Als
Page 15 and 16: sin 1 sin 2 sin 1 sin 2 sin 1 sin 2
Page 17 and 18: Now, let us assume that it is true
Page 19 and 20: BOOK REVIEWS Edited by ANDY LIU 275
Page 21 and 22: Hence a0 + b0 m2 = a0 , b0 m1 = c0
Page 23 and 24: 279 take the primitive self-altitud
Page 25 and 26: THE SKOLIAD CORNER No. 31 R.E. Wood
Page 27 and 28: 283 12. If C Celsius is the same te
Page 29 and 30: A B C D E (a) A (b) B (c) C (d) D (
Page 31 and 32: 287 (quadratic non-residue), then f
Page 33 and 34: High School Problems 289 Editor: Ri
Page 35 and 36: The Pentagram Theorem Hiroshi Koter
Page 37: and so by (3), and so by (4), Simil
Page 41 and 42: 297 position in one of the three pi
Page 43 and 44: 299 6. A small school with 50 pupil
Page 45 and 46: PROBLEMS 301 Problem proposals and
Page 47 and 48: 303 2355. Proposed by G.P. Henderso
Page 49 and 50: SOLUTIONS 305 No problem is ever pe
Page 51 and 52: We shall also show that r 9 R 2r 9
Page 53 and 54: 309 ( ; ; ) 2 D", then one of the n
Page 55 and 56: Now (4) becomes H( ):=cot + 1, k 3
Page 57 and 58: 313 [Editor's note: A triangle, X =
Page 59 and 60: 315 Editor's comment. Even though t
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Page 63 and 64: 319 AD = a , b; AE = a , c, and ED

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