Question

A circle is inscribed in another. The radius of the large circle is R. The radius of the small circle is r. The areas of the shaded region and the white region are equal. which is greater R/r or 1.5 ???

Answer 1

Figure?

Answer 2

R^2-r^2=r^2 yes? but then I cannot how to compare with 1.5 ???

Answer 3

oh..correct !
R^2 = 2r^2
take square root on both sides.

Answer 4

by adding r^2 on both sides....

Answer 5

what you get when you take square root on both sides of R^2=2r^2 ?

Answer 6

Large circle: AL = (pi)R^2
Small circle: AS = (pi)r^2
Area of shaded ring: AR = (pi)R^2 - (pi)r^2 = (pi)(R^2 -r^2)
Areas are equal: (pi)r^2 = (pi)(R^2 -r^2)
r^2 = R^2 - r^2
2r^2 = R^2
R^2/r^2 = 2
R/r = sqrt(2)

Answer 7

and sqrt 2 = 1.414

Answer 8

ok i got it, thanks :))

Answer 9

wlcm