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Question Number 4196 by Rasheed Soomro last updated on 31/Dec/15

  Q#4140 is again asked with following changes:  a always moves towards b′ (instead of b),  b always moves towards c′ (instead of c),  c always moves towards  d′ (instead of d),   d always moves towards  a′ (instead of a),  where a′,b′,c′ and d′ are midpoints of line  segments ab, bc, cd  and  da respectively.

$$\:\:\mathrm{Q}#\mathrm{4140}\:\mathrm{is}\:\mathrm{again}\:\mathrm{asked}\:\mathrm{with}\:\mathrm{following}\:\mathrm{changes}: \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{b}}\right), \\ $$$$\boldsymbol{\mathrm{b}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{c}}\right), \\ $$$$\boldsymbol{\mathrm{c}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{d}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{d}}\right),\: \\ $$$$\boldsymbol{\mathrm{d}}\:\mathrm{always}\:\mathrm{moves}\:\mathrm{towards}\:\:\boldsymbol{\mathrm{a}}'\:\left({instead}\:{of}\:\boldsymbol{\mathrm{a}}\right), \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{a}}',\boldsymbol{\mathrm{b}}',\boldsymbol{\mathrm{c}}'\:\mathrm{and}\:\boldsymbol{\mathrm{d}}'\:\mathrm{are}\:\mathrm{midpoints}\:\mathrm{of}\:\mathrm{line} \\ $$$$\mathrm{segments}\:\boldsymbol{\mathrm{ab}},\:\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cd}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{da}}\:\mathrm{respectively}. \\ $$

Commented by Rasheed Soomro last updated on 31/Dec/15

Also compare time-taken in travel from start  to meeting (if they will meet) between the  questions.

$$\mathrm{Also}\:\mathrm{compare}\:\mathrm{time}-\mathrm{taken}\:\mathrm{in}\:\mathrm{travel}\:\mathrm{from}\:\mathrm{start} \\ $$$$\mathrm{to}\:\mathrm{meeting}\:\left(\mathrm{if}\:\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\right)\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{questions}. \\ $$

Commented by RasheedSindhi last updated on 01/Jan/16

Whatif b′ is on bc^(↔)  beyond the b,  c′ is on cd^(↔)  beyond thd c...for example  when bb′=bc, cc′=cd....

$$\mathrm{Whatif}\:\boldsymbol{\mathrm{b}}'\:\mathrm{is}\:\mathrm{on}\:\overset{\leftrightarrow} {\boldsymbol{\mathrm{bc}}}\:\mathrm{beyond}\:\mathrm{the}\:\boldsymbol{\mathrm{b}}, \\ $$$$\boldsymbol{\mathrm{c}}'\:\mathrm{is}\:\mathrm{on}\:\overset{\leftrightarrow} {\boldsymbol{\mathrm{cd}}}\:\mathrm{beyond}\:\mathrm{thd}\:\boldsymbol{\mathrm{c}}...\mathrm{for}\:\mathrm{example} \\ $$$$\mathrm{when}\:\boldsymbol{\mathrm{bb}}'=\boldsymbol{\mathrm{bc}},\:\boldsymbol{\mathrm{cc}}'=\boldsymbol{\mathrm{cd}}.... \\ $$

Commented by Rasheed Soomro last updated on 01/Jan/16

Commented by Rasheed Soomro last updated on 01/Jan/16

According to diagram  A,B,D,C  arefour persons moving to  G,H,E,F points respectively.

$${According}\:{to}\:{diagram} \\ $$$$\boldsymbol{\mathrm{A}},\boldsymbol{\mathrm{B}},\boldsymbol{\mathrm{D}},\boldsymbol{\mathrm{C}}\:\:{arefour}\:{persons}\:{moving}\:{to} \\ $$$$\boldsymbol{\mathrm{G}},\boldsymbol{\mathrm{H}},\boldsymbol{\mathrm{E}},\boldsymbol{\mathrm{F}}\:{points}\:{respectively}. \\ $$

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