Circles

Link of the Day

Would you like a break from school right around now?  Students in Chicago are getting just that.  They have had over a week without school as teachers strike over conflicts with the mayor concerning the best methods to improve underperforming schools.  Take a look at this current event and think about how you could use details from this story in an excellent example for your essay that shows SAT graders that you are well informed.  Make a list of all of the broad themes that this story illustrates, such as change, education, other points of view, adversity, success (Can it be disastrous?), how to question those in authority, and many many more. 

9/18 Circles

Read the following SAT test question and then select the correct answer. 

 

The circle above has center P. Given segments of the following lengths, which is the length of the longest one that can be placed entirely inside this circle?

Your bottom line is the longest length that can be placed inside a circle.  Before you look at any of the numbers in this particular problem, think about circles in general.  You know that a line segment, within the circle, with both end points on the circle is called a chord.  The longest chord will always be the diameter of the circle.

You have enough information to find the diameter of this circle.  The line labeled 4 is actually the radius of the circle.  A radius is half of the diameter, so multiply the radius by 2 in order to find the diameter: 2 × 4 = 8. 

This is the part of the problem where you loop back and see whether your answer matches the bottom line.  You found the diameter of the circle, but that is not actually the bottom line.  A diameter is a chord that touches the circle’s edges.  You were asked to find the longest length that can be placed entirely in the circle.  In order for the length you found to not touch the circle, it must be slightly smaller than 8, perhaps 7.9999999.  Now look down at your answer choices.

(A) 6.99

(B) 7.00

(C) 7.99

(D) 8.10

(E) 14.00

The correct answer is (C).  

Notice that you did not need to use all of the information that you were given in this problem.  Always take the time to read the question carefully so that you will not be confused or distracted by extra information, such as the chord labeled 7 in this problem.

On sat.collegeboard.org, 62% of the responses were correct.

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