PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters areas A and B are shaded A/B is equal to 

Asked by rushabh123 | 7th Feb, 2019, 10:15: AM

Expert Answer:

Let r be the radius of small circles given in the quetion-figure.
The marked area as B in the figure given in question is twice the shaded area shown in above figure.
Shaded area shown in above figure = Area of quarter circle - area of triangle OXY = (π/4)r2 - (1/2)r2 = [ (π-2)/4 ]r2
Hence marked area as B in the question-figure =  [ (π-2)/2 ]r2 ......................(1)
marked area as A in question-figure = (1/4)[ area of outer circle - { (4×area of inner circle) - (all the areas marked as B) } ]
marked area as A in question-figure = (1/4)[ π(2r)2 - (4×πr2) + 4×{ (π-2)/2 }r2 ] = [ (π-2)/2 ]r2 ............(2)
By comparing eqn.(1) and eqn.(2), we see the area marked as A is same as the area marked as B.
Hence the required ratio of areas = 1

Answered by Thiyagarajan K | 7th Feb, 2019, 01:32: PM

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