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What is the area of the large square?
let the distance between length 4 and center of the figure be x
let the distance between length 6 and center of the figure be y
then 4+x=6+y or x=y+2 (1)
form the inner circle (6+y)*y=x*x (2)
from (1) and (2) x=4 and y=2
therefore length of smaller square is 8 and of larger square 16
thus area of larger square is 256
Let the radius of large circle = r
For small circle apply intersection of the chord theorem . That is When two chords intersect each other inside a circle, the products of their segments are equal.
r * (r-6) = (r-4) * (r-4) solving r = 8
So area = 2r * 2r = 256
this is a theorem.
Each side of a square is divided into three equal parts by two points on it, which are connected as shown in the diagram below (that is not drawn to scale).
If the smaller, red square has an area of 800, what is the area of the large square?
What is the ratio of area of large square to the area of smaller square in the following image?
What is the area of the blue region in the following image?
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