MathDB
Circle Inscribed In Circle

Source: 1964 AHSME #13

October 20, 2012
ratioAMC

Problem Statement

A circle is inscribed in a triangle with side lengths 88, 1313, and 1717. Let the segments of the side of length 88, made by a point of tangency, be rr and ss, with r<sr<s. What is the ratio r:sr:s?
<spanclass=latexbold>(A)</span> 1:3<spanclass=latexbold>(B)</span> 2:5<spanclass=latexbold>(C)</span> 1:2<spanclass=latexbold>(D)</span> 2:3<spanclass=latexbold>(E)</span> 3:4{{ <span class='latex-bold'>(A)</span>\ 1:3 \qquad<span class='latex-bold'>(B)</span>\ 2:5 \qquad<span class='latex-bold'>(C)</span>\ 1:2 \qquad<span class='latex-bold'>(D)</span>\ 2:3 }\qquad<span class='latex-bold'>(E)</span>\ 3:4 }