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Question Number 64909 by Tawa1 last updated on 23/Jul/19

Commented by MJS last updated on 23/Jul/19

the picture shows 2 circles, so the given  numbers don′t fit. obviously the right must  be greater than the above/below numbers

thepictureshows2circles,sothegivennumbersdontfit.obviouslytherightmustbegreaterthantheabove/belownumbers

Commented by Tawa1 last updated on 23/Jul/19

God bless you sir, i get.  I will ask you to give me questions on shaded area when am   ready done with your solution and sir mrW solution and sir Ajfour

Godblessyousir,iget.IwillaskyoutogivemequestionsonshadedareawhenamreadydonewithyoursolutionandsirmrWsolutionandsirAjfour

Answered by MJS last updated on 23/Jul/19

if we exchange 10 ⇌ 18  the big circle  x^2 +y^2 =r^2  ⇒ y=±(√(r^2 −x^2 ))  the small circle  (x+9)^2 +y^2 =(r−9)^2  ⇒ y=±(√((r−9)^2 −(x+9)^2 ))  let′s use the upper half circles  y_1 =(√(r^2 −x^2 ))  y_2 =(√((r−9)^2 −(x+9)^2 ))  at x=0: y_1 −y_2 =10 ⇒ y_2 =y_1 −10  y_1 =r  y_2 =(√(r(r−18)))  (√(r(r−18)))=r−10  r(r−18)=(r−10)^2   2r−100=0  r=50  ⇒ the small circle has radius 50−9=41  ⇒ the shaded area = 50^2 π−41^2 π=819π

ifweexchange1018thebigcirclex2+y2=r2y=±r2x2thesmallcircle(x+9)2+y2=(r9)2y=±(r9)2(x+9)2letsusetheupperhalfcirclesy1=r2x2y2=(r9)2(x+9)2atx=0:y1y2=10y2=y110y1=ry2=r(r18)r(r18)=r10r(r18)=(r10)22r100=0r=50thesmallcirclehasradius509=41theshadedarea=502π412π=819π

Commented by Tawa1 last updated on 23/Jul/19

God bless you sir

Godblessyousir

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