What is the ratio of the Blue area to the Yellow area to the Red area? (A quarter-circle is constructed. A semi-circle is constructed on the radius of the quarter circle. Finally, a circle of maximum radius is inscribed in the semi-circle)

Guest Jan 12, 2020

#1**+1 **

Orange area is 1/4 pi r^2 (well, the WHOLE quadrant is)

yellow area is 1/2 pi (1/2 r)^2 ( this is the semicircle area....blue will be subtracted shortly)

blue area is pi (1/4r)^2

Divide all be pi

Blue area : yellow semi-circle - blue circle : red quarter - yellow semicircle

1/16 r^2 : 1/8 r^2 - 1/16r^2 : 1/4 r^2 -1/8r^2 Divide out the r^2 and simplify

1/16 : 1/16 : 1/8

1/16 : 1/16 : 1/8

1:1:2

** CORRECTED ! THANX to Dragan who noticed my error.....I originally listed the red as an entire quarter and the yellow as a full semicircle !**

ElectricPavlov Jan 12, 2020