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
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.)
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