Question

a square is increased in a circle of diameter D if one side of the blue square is the diagonal of the Red Square what is the ratio of the area of the smaller square to the area of circle​

Answer 1

Answer:

PQRS is a square inscribed in a circle of diameter

SQ=d which in turn has been inscribed in the square ABCD.

To find out whether ar.ABCD=4×ar.PQRS or not.

SQ=d is the diagonal of the square PQRS

Since the diameter of a circle circumscribing a square = diagonal of the same square.

∴  Any side of PQRS=PQ=2d2 

∴ar.PQRS=2d2

Again SD=d= one side of ABCD=AD.

∴ar.ABCD=AD2=d2

So, ar.PQRSar.ABCD=2d2d2=2

Ratio of area of outer square to the area of inner square is 2:1.