<p>A circle O is inscribed in right triangle ABC. If AB=3, AC=4, and the radius of the circle is r, what is the value of r?</p>
<p>The answe goes like this. The area of the triangle is 6. And, he area=1/2(5r+4r+3r)=6r. So, 6r=6 and r=1. </p>
<p>Can someone explain how they got the second area formula? How did they get 1/2(5r+4r+3r)?</p>
<p>This does not look like an SAT I problem. It requires too much specialized outside math knowledge. If you want a good explanation of where that second formula comes from, go to <a href=“http://www.bobbymcr.com/main/math/incircle.pdf[/url]”>http://www.bobbymcr.com/main/math/incircle.pdf</a></p>
<p>and read the description there</p>
<p>This question is beyond SAT I test. I have written an explanation in the following link:</p>
<p>[Answer-06052013</a> - Dabral’s library](<a href=“http://www.screencast.com/t/lFhhYYK16S]Answer-06052013”>http://www.screencast.com/t/lFhhYYK16S)</p>
<p>Not a SAT problem … yet! It is still, however, an interesting problem.</p>
<p>Fwiw, finding the radius of a circle inscribed in a right triangle has a simple formula:</p>
<p>r = (a + b - c) / 2 where a and b are the two small sides</p>
<p>In this case, that is 3+4-5 divided by 2 or 2/2 or 1. We know that the area of the triangle is 2x3 or 6. </p>
<p>And, we could also use r = a*b/(a+b+c, which yields 12 / 12 = 1 </p>
<p>With those little gems of formulaes, this question is trivial. I’d say that it is a GREAT SAT question in the making. :)</p>
<p>PS What about the relation between the circumference of the circle and the perimeter of the triangle. The diameter is obviously a + b - c (2 in this case) and the perimeter of the triangle, which is 12.</p>
<p>WAY too complicated for an SAT problem…</p>