SOLUTION: Find the area of the larger circle in {{{ cm^2 }}} if {{{ r=sqrt(2) }}} cm. https://ibb.co/PjYkRmL

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Question 1199330: Find the area of the larger circle in if cm.
https://ibb.co/PjYkRmL

Found 3 solutions by greenestamps, ikleyn, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


ANSWER: C

To see this, draw segments from the center of the small circle to the center of the large circle, and to the points of tangency of the small circle with the x- and y-axes. Use those to determine that the radius of the large circle is



Then the area of the circle is (pi)(r^2) = , answer C.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

I just solved this problem and answered this question several days ago.

See the link

https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1199274.html



Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

 

To find the area of the larger circle, we need to find its radius.

The red and green triangles are similar 45-45-90 isosceles right triangles.
Since the green hypotenuse is given to be , it is a standard
1-1- isosceles right triangle, and its legs are 1 each.

The radius of the larger circle is the sum of the red and green hypotenuses.
The green hypotenuse is  and is a radius of the small circle, So, the 
vertical red side is also , because it is also a radius of the smaller circle. 

We set up a proportion between the sides of the two similar triangles:





Cross-multiply and get







Using ,

 cm2

Edwin
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