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Question
largest quad in circle
in a circle with radius 1 centered at the origin, two perpendicular lines are drawn that intersect at (0.5,0) what is the area of the largest quad that the intersections of these two lines with the circle forms?
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by: d343sevenPosted on 2004-12-31 at 20:56:16ID: 12934920
Hi djiangr.
i am pretty sure that the largest area occurs when the lengths of the lines are exactly the same (same thing as product of numbers...closer=bigger). the diagonals' product * 1/2 is the area since they are perpedicular.
since they will have the same length, a 45 degree angle is made by each line with the x axis. =>slope = 1
so the equation of one line is y=x-1/2
the equation of the circle is ofcourse x^2+y^2=1
solving these two equations for x (or y, just do one) will give something like "a plus or minus b"--which will be the two intersections with the circle
thus, finding the difference will give you one leg of a 45-45-90 right triangle, with hypotenuse being the lenght you are looking for. so to find that, multiply by root 2, and you have rt(2)((a+b)-(a-b)) = rt(2)(2b), and then you can square that and divide by 2 to get the answer, the area of the quad.
try to get it