AN EXTREME BEAST OF A MATH PROBLEM (scary even)

<p>oh hell.....some 1 ? an easier method?</p>

<p>asdfasdfasdf</p>

<p>Okay. Since the segment is tangent to the circle, that means it's perpendicular to the radius. The segment's slope is -1. The circle is tangent to both axes and the radius is one, so it's like the circle is backed up into the corner of the axes. Now, just be like "where the hell can that segment touch the circle?" If you imagine it, you'll see that the line has to hit the upper right side of the circle. Then it's like "what point is that?" Remember your unit circle, and you know that it's answer C. I don't know how to explain it other than that.</p>

<p>so you know that the segment has a slope of -1, therefore it must be perpendicular to the line that has a slope of 1, which is x=y. Draw the line of the figure. Then you know that the segment is tangent at t, if you drew the line, then the only two possible positions in which the segment could be become obvious - either on the upper right or the lower left. Since the answer choices gives you the "big" coordinates, then you can assume that it's asking for the upper right one. The next part is kinda hard to explain... well, draw the horizontal diameter of the circle, and draw a line from the tangent point down to the diameter, perpendicularly. And this makes a 45-45-90 triangle. You know the sides are equal because of the slope 1. Rise over run = 1 therefore rise=run. And use the properties of a 45-45-90 tirangle to get the answer.</p>

<p>Well, i still dont even understand the solution, but here it goes:</p>

<p>EXPLANATION
Since O has a radius of 1, the center of the circle is at (1,1). If segment AB has a slope of -1, that means that the line from the center of the circle to point t must have a slope of 1. (In other words a 45 degree angle) Make this radius the hypotenuse of a 45:45:90 right triangle. The other two sides are parallel to the axes. Since the hypotenuse has a length of 1, the two legs must have a length of (1/squareroot(2)). The x value of the point t is the radius plus the bottom of the triangle, which is 1+1/(squareroot(2)) None of the answer choices have this as an x-value. (Try rationalizing so the side equals (square root (2))/2...This makes the value 1+square root (2)/2. The y-value has to be the same value as the x, so therefore the answer is C</p>

<p>^ it's much better worded than my version.</p>

<p>^ mine was more colloquial :]</p>

<p>^i dont understant....ah!</p>

<p>which part confuses you? try drawing the circle and everything I told you to draw. btw the center of the circle is 1,1 in case you are wondering. (I didn't mention it in my post)</p>

<p>yeah, i know, but what part is the 45:45:90 triangle???</p>

<p>I think I got it... I drew up a diagram, here:</p>

<p>

<a href="http://img.photobucket.com/albums/v634/sushiISgood/quest.jpg%5B/img%5D"&gt;http://img.photobucket.com/albums/v634/sushiISgood/quest.jpg

</a></p>

<p>......if this is a sat l que...then still i have a lot left to work on... :(</p>

<p>Process of elimination could have led you to the right answer too.</p>

<p>thank you yeti crab</p>

<p>yeah gluttony....i just wish it never comes up again</p>

<p>it's formed by the horizontal diameter you draw for the circle, the line x=y, and the line drawn from t down to the diameter perpendicularly. t is the upper right tangent point.</p>

<p>Oh okay. I just didn't convert Sqrt of 1/2 to Sqrt(2)/2 lol</p>

<p>yeah. the diagram works better lol</p>

<p>oh..........thanks alot u guys... i understand it now</p>

<p>No problem, gluttony. :D</p>

<p>I was confused at first because I first drew the triangles facing the wrong way.</p>