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Given4ABC, let P,Q, andR be points on sides BC,AC, andAB, respectively, with RQ∦BC, and so that AP,BQ and CR are concurrent cevians. Extend the line segment RQ to meet sideline BC at point S(see figure below.) Prove that xz=y(x+y+z) where x=BP,y=P C,z=CS.(Hint: Use Ceva’s and Menelaus’ theorems.)

Given4ABC, let P,Q, andR be points on sides BC,AC, andAB, respectively, with RQ∦BC, and so that AP,BQ and CR are concurrent cevians. Extend the line segment RQ to meet sideline BC at point S(see figure below.) Prove that xz=y(x+y+z) where x=BP,y=P C,z=CS.(Hint: Use Ceva’s and Menelaus’ theorems.)

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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Given4ABC, let P,Q, andR be points on sides BC,AC, andAB, respectively, with RQ∦BC, and so that AP,BQ and CR are concurrent cevians. Extend the line segment RQ to meet sideline BC at point S(see figure below.) Prove that xz=y(x+y+z) where x=BP,y=P C,z=CS.(Hint: Use Ceva’s and Menelaus’ theorems.)

Given AABC, let P, Q, and R be points on sides BC, AC, and AB, respectively, with RQ { BC, and so that AP, BQ and CR are concurrent cevians. Extend the line segment RQ to meet sideline BC at point S (see figure below.) Prove that xz = y(x + y + z) where x = BP, y = PC, z = CS. (Hint: Use Ceva's and Menelaus' theorems.) A R Q B S РУС
Transcribed Image Text:Given AABC, let P, Q, and R be points on sides BC, AC, and AB, respectively, with RQ { BC, and so that AP, BQ and CR are concurrent cevians. Extend the line segment RQ to meet sideline BC at point S (see figure below.) Prove that xz = y(x + y + z) where x = BP, y = PC, z = CS. (Hint: Use Ceva's and Menelaus' theorems.) A R Q B S РУС
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