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Question Number 177586 by aurpeyz last updated on 07/Oct/22

Commented by aurpeyz last updated on 07/Oct/22

$$plshelp.thequestionisgivingmeheadache$$

Commented by mr W last updated on 07/Oct/22

$$thequalityoftheimageisgivingme$$$$headache:\left\{\right)$$

Commented by Ar Brandon last updated on 07/Oct/22

��

Commented by aurpeyz last updated on 07/Oct/22

$$thankyouforsolvingit$$

Answered by mr W last updated on 07/Oct/22

$$quantityAisthelinesegmentAB.$$$$AB=2r\times \sin \frac{\mathrm{\angle }AOB}{2}$$$$0<\mathrm{\angle }AOB<\frac{\pi }{2}$$$$0<\frac{\mathrm{\angle }AOB}{2}<\frac{\pi }{4}$$$$0<\sin \frac{\mathrm{\angle }AOB}{2}<\frac{\sqrt{2}}{2}$$$$0<2r\sin \frac{\mathrm{\angle }AOB}{2}<\sqrt{2}r<1.5r$$$$\Rightarrow quantityBisgreaterthanA.$$

Commented by mr W last updated on 07/Oct/22

$$ifquantityAisthearcsegment\stackrel{⌢}{AB}.$$$$\stackrel{⌢}{AB}=\mathrm{\angle }{AOB}_{inrad}\times r$$$$0<\mathrm{\angle }AOB<\frac{\pi }{2}$$$$\Rightarrow 0<\stackrel{⌢}{AB}<\frac{\pi }{2}r\approx 1.57r$$$$quantityAisbetween0and1.57r.$$$$quantityBis1.5r.$$$$thatmeanswithgiveninformation$$$$youcannotsaywhichisgreater.$$

Commented by aurpeyz last updated on 07/Oct/22

$$thisiswhattheychoseastheanswer$$

Commented by aurpeyz last updated on 07/Oct/22

$$isthelengthoflinesegmentABthesameaslengthofarcinthiscase?$$

Commented by mr W last updated on 07/Oct/22

$$certainlyno!$$$$\stackrel{⌢}{AB}>ABalways!$$

Commented by mr W last updated on 07/Oct/22

$$theyfromthebookarewrong!since$$$$inthequestionquantityAistheline$$$$segmentAB,veryclear!$$

Commented by aurpeyz last updated on 07/Oct/22

$$sotherightanswerisB.yourfirstsolution?$$

Commented by mr W last updated on 07/Oct/22

$$yes.$$

Commented by aurpeyz last updated on 07/Oct/22

$$thanks$$

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