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From Oct 01 SAT, posted elsewhere on the board.

Sec 2 #22
[involves drawing] In the figure above, side AC of triangle ABC is on line l. What is x in terms of k?
a) 60 - k = answer...I put 60 + k

Sec 6
10) If 3 diff. circles are drawn on a piece of paper, how many points can be in common to all three?
c) two
anyway to figure that out besides drawing?

Thanks for any help...

By Curiousone (Curiousone) on Thursday, March 27, 2003 - 09:26 pm: Edit

bump
(edited message)

By Curiousone (Curiousone) on Thursday, March 27, 2003 - 09:29 pm: Edit

OK, I feel retarded. I got the analogy when I posted it. Nevermind.

By Curiousone (Curiousone) on Thursday, March 27, 2003 - 09:29 pm: Edit

OK, I feel retarded. I got the analogy when I posted it. Nevermind.

By Xiggi (Xiggi) on Thursday, March 27, 2003 - 10:32 pm: Edit

Since exactly one circle is determined by three points not all on the same line, there is at most one circle that can be drawn through any set of three points.


This means that if three different circles are drawn on a piece of paper, no more than two points can be common to all three.


To see that two points are, indeed, possible, first start with a pair of circles that have two points P and Q in common. Another circle can be drawn through these two points. Click the link to see a diagram.

http://www.collegeboard.com/sat/center/q1001/fig1001/m_r_1a.gif


Since it has been shown that two points can be common to three different circles and that no more than two points can be common, the correct answer is C.

By Xiggi (Xiggi) on Thursday, March 27, 2003 - 10:41 pm: Edit

Sec 2 #22
[involves drawing] In the figure above, side AC of triangle ABC is on line l. What is x in terms of k?
a) 60 - k = answer...I put 60 + k

You need to look at the figure.

1. Recognize that the inside angle C of ABC is 60 since its complement is 120.

2. Now you know that two angles of ABC are x (for B) and 60 for C.

3 Now look at the exterior angle of A is also equal to B + C ===> So (120-k)=60 + x

4. Reduce 120-k=60 + x and you are left with the answer and that is 60-k = x

So, it is A.

By Curiousone (Curiousone) on Thursday, March 27, 2003 - 10:51 pm: Edit

I had realized that 120-k and the interior angle of A and 120 and the interior angle of C were supplements, but for some reason, I guess I had some careless mistake in the arithmetic that when I got rid of the parentheses somewhere caused me to change one of the negatives to a positive when I shouldn't have...

Anyway, thanks for the help!

By Xiggi (Xiggi) on Friday, March 28, 2003 - 11:00 am: Edit

You also corrected me.

I used "complement" when it was supposed to be "supplement".