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Question Number 48777 by naka3546 last updated on 28/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

yes sir i found my mistake...

$${yes}\:{sir}\:{i}\:{found}\:{my}\:{mistake}... \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18

Area of big white porion found  now from triangle △BOC  and sector OBXCO  calculating small white area  pls wait=...

$${Area}\:{of}\:{big}\:{white}\:{porion}\:{found} \\ $$$${now}\:{from}\:{triangle}\:\bigtriangleup{BOC}\:\:{and}\:{sector}\:{OBXCO} \\ $$$${calculating}\:{small}\:{white}\:{area} \\ $$$${pls}\:{wait}=... \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

who red marked and why

$${who}\:{red}\:{marked}\:{and}\:{why} \\ $$

Commented by mr W last updated on 28/Nov/18

green area=white area=((area of circle)/2)

$${green}\:{area}={white}\:{area}=\frac{{area}\:{of}\:{circle}}{\mathrm{2}} \\ $$

Commented by mr W last updated on 28/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

before pointing fingure better you judge yourself  OK i am leaving the forum...

$${before}\:{pointing}\:{fingure}\:{better}\:{you}\:{judge}\:{yourself} \\ $$$$\boldsymbol{{O}}{K}\:{i}\:{am}\:{leaving}\:{the}\:{forum}... \\ $$

Commented by mr W last updated on 29/Nov/18

thank you sir!  the question is quite general, but in  your calculation you have assumed  that the thing is symmetric. in your  first chart you assumed AC=AD and  BC=ED, so you got BC=R sin ((45°)/2). but  the question doesn′t mean this special  case. i.e. generally AC≠AD and   BC≠ED≠R sin ((45°)/2).  that′s to say, to be exact, your calculation   is only a confirmation for the statement  that green area = circle area / 2 in a  special case, but it′s not the general  proof for the statement.

$${thank}\:{you}\:{sir}! \\ $$$${the}\:{question}\:{is}\:{quite}\:{general},\:{but}\:{in} \\ $$$${your}\:{calculation}\:{you}\:{have}\:{assumed} \\ $$$${that}\:{the}\:{thing}\:{is}\:{symmetric}.\:{in}\:{your} \\ $$$${first}\:{chart}\:{you}\:{assumed}\:{AC}={AD}\:{and} \\ $$$${BC}={ED},\:{so}\:{you}\:{got}\:{BC}={R}\:\mathrm{sin}\:\frac{\mathrm{45}°}{\mathrm{2}}.\:{but} \\ $$$${the}\:{question}\:{doesn}'{t}\:{mean}\:{this}\:{special} \\ $$$${case}.\:{i}.{e}.\:{generally}\:{AC}\neq{AD}\:{and}\: \\ $$$${BC}\neq{ED}\neq{R}\:\mathrm{sin}\:\frac{\mathrm{45}°}{\mathrm{2}}. \\ $$$${that}'{s}\:{to}\:{say},\:{to}\:{be}\:{exact},\:{your}\:{calculation}\: \\ $$$${is}\:{only}\:{a}\:{confirmation}\:{for}\:{the}\:{statement} \\ $$$${that}\:{green}\:{area}\:=\:{circle}\:{area}\:/\:\mathrm{2}\:{in}\:{a} \\ $$$${special}\:{case},\:{but}\:{it}'{s}\:{not}\:{the}\:{general} \\ $$$${proof}\:{for}\:{the}\:{statement}. \\ $$

Commented by mr W last updated on 29/Nov/18

I think someone red marked your posts  by mistake. in fact he just wanted to give  your posts a Like. this happens   frequentlly in the forum. so don′t take  it serious.

$${I}\:{think}\:{someone}\:{red}\:{marked}\:{your}\:{posts} \\ $$$${by}\:{mistake}.\:{in}\:{fact}\:{he}\:{just}\:{wanted}\:{to}\:{give} \\ $$$${your}\:{posts}\:{a}\:{Like}.\:{this}\:{happens}\: \\ $$$${frequentlly}\:{in}\:{the}\:{forum}.\:{so}\:{don}'{t}\:{take} \\ $$$${it}\:{serious}. \\ $$

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