MathDB
Distance Between Circumcircle and Incircle

Source:

January 15, 2009
geometrycircumcircleanalytic geometryinradiusincentertrigonometryPythagorean Theorem

Problem Statement

A triangle with sides of 5 5, 12 12, and 13 13 has both an inscibed and a circumscribed circle. What is the distance between the centers of those circles? <spanclass=′latex−bold′>(A)</span> 352<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 15<spanclass=′latex−bold′>(D)</span> 652<spanclass=′latex−bold′>(E)</span> 92 <span class='latex-bold'>(A)</span>\ \frac{3\sqrt{5}}{2}\qquad <span class='latex-bold'>(B)</span>\ \frac{7}{2}\qquad <span class='latex-bold'>(C)</span>\ \sqrt{15}\qquad <span class='latex-bold'>(D)</span>\ \frac{\sqrt{65}}{2}\qquad <span class='latex-bold'>(E)</span>\ \frac{9}{2}
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