What is the Area Not Shared by the Circles?
Date: 3 Mar 1995 10:01:35 -0500 From: Mary Basse Subject: Geometry When I was taking the SAT test, I ran across this problem. Will you please help me? Two circles intersect such that their centers and their points of intersection form a square with each side equal to 3. What is the total area of the sections of the square that are not shared by both circles? Thank you. Russell email@example.com
Date: 3 Mar 1995 10:41:53 -0500 From: Dr. Ken Subject: Re: Geometry Hello there! This is one of the nicer problems I've seen on the SAT (I'm ordinarily not a fan of their math problems, or even their answers; they have been known to use incorrect answers as correct). Here's a hint on how you might approach it. You know that the area of the square must be 9, right? So what we want to do is subtract the football-shaped region in the middle. So how do we find its area? Well, here's what I'd do. You can find the area of the part of the square that makes up 1/4 of one of the circles, right? If you add two of these regions together, you will get the area of the square plus some overlap. This overlap is the area of the football. And once you've found the area of the football, you can subtract it from 9 to find out the answer to the problem. Thanks for the question, and let us know if you need some more help! -Ken "Dr." Math
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