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8. Let AL, BM, and CN be three concurrent Cevians of AABC. Use Menelaus' theorem to prove that AN BL CM x = 1. (Hint: Apply Menelaus' theorem to the two triangles associated to transversals BFM [points NB LC MA and M are collinear] and AFL [points A, F, and L are collinear]). AH + Cl be thi

8. Let AL, BM, and CN be three concurrent Cevians of AABC. Use Menelaus' theorem to prove that AN BL CM x = 1. (Hint: Apply Menelaus' theorem to the two triangles associated to transversals BFM [points NB LC MA and M are collinear] and AFL [points A, F, and L are collinear]). AH + Cl be thi

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Let AL, BM, and CN be three concurrent Cevians of AABC. Use Menelaus' theorem to prove that AN BLCM X x A B -= 1. (Hint: Apply Menelaus' theorem to the two triangles associated to transversals BFM [points NB LC MA and M are collinear] and AFL [points A, F, and L are collinear]).: M F N B Let, AL, BM,+ EAS! be the concurrent devians, we to prove that AN. BL LC Applying Mentlaus theor Мерували A ABM ABF we obtain " ewrite as AN NB FM MA = -1₁ we MC = -10 BF pplying Menalaus, theren 13 FM" FM CA-1 o transversal AFT + AALB we obtain AE.LG.CM ve can rewrite as AE LC, BM = =+ •bf.m FL LB hus, NA AN NB FM MA = AF, LB.CM FL ма FL
Transcribed Image Text:8. Let AL, BM, and CN be three concurrent Cevians of AABC. Use Menelaus' theorem to prove that AN BLCM X x A B -= 1. (Hint: Apply Menelaus' theorem to the two triangles associated to transversals BFM [points NB LC MA and M are collinear] and AFL [points A, F, and L are collinear]).: M F N B Let, AL, BM,+ EAS! be the concurrent devians, we to prove that AN. BL LC Applying Mentlaus theor Мерували A ABM ABF we obtain " ewrite as AN NB FM MA = -1₁ we MC = -10 BF pplying Menalaus, theren 13 FM" FM CA-1 o transversal AFT + AALB we obtain AE.LG.CM ve can rewrite as AE LC, BM = =+ •bf.m FL LB hus, NA AN NB FM MA = AF, LB.CM FL ма FL
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