A carpenter wishes to cut four equal circles from a circular piece of wood whose area is equal to 9 - Maths - Circles

Question

A carpenter wishes to cut four equal circles from a circular piece
of wood whose area is equal to 9 pie sq metre he wants these
circles of wood to be the largest that can possibly be cut from it
Measure of radius of each of the four new circles

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

Let R be the radius of circular piece of woodand r be the radius of smaller circles

Now,OP=R , radius of larger circlePB=r , radius of smaller circleOB=R-rOA=OC    Tangents drawn from same external points are equal∠OCB=∠OAB=90°     Radius makes 90° angle with tangent⇒OA ∥ CB and OC ∥ AB⇒OABC is a parallelogram
⇒OA=BC and OC=ABOA=BC=rNow,In △OAB , applying pythagoras theoremOB2=OA2+AB2R-r2=r2+r2R2-2rR+r2=2r2r2+2rR-R2=0r=-2R±4R2+4R22=-2R±22R2=-R±2Rr=-R+2R   or  r=-R-2RRadius can't be negative
So, r=-R+2R Now,Area of larger circle=9π m2πR2=9πR=3 m
So,r=-3+32=3 2-1 m
Radius of each of the four new circle is 3 2-1 m
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A carpenter wishes to cut four equal circles from a circular piece of wood whose area is equal to 9 pie sq.metre.he wants these circles of wood to be the largest that can possibly be cut from it.Measure of radius of each of the four new circles.