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, withRQ { BC, and so that AP, BQ and CR are concurrent cevians. Extend the line segment RQ tomeet 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.)ARQBSРУС

Name: Given4ABC, let P,Q, andR be points on sides BC,AC, andAB, respectively
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Description: 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,

Consider the equationLet ABC be a traingle ,let P,Q,R be a point on line BC,CA,AB respectively lines AP,BQ,CRBPPC,CQQAARRB =1 where length are directed this also work on the reciprocal of each of the ratio as the reciprocal of 1is 1The proof using Ceva theorem is proved.

Answered: Given4ABC, let P,Q, andR be points on…

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

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