MathDB
Circumcenter and Incenters

Source: 2018 AMC 12B #21

February 16, 2018
geometrycircumcircleincenter2018 AMC 12B2018 AMCAMC 12

Problem Statement

In ABC\triangle{ABC} with side lengths AB=13AB = 13, AC=12AC = 12, and BC=5BC = 5, let OO and II denote the circumcenter and incenter, respectively. A circle with center MM is tangent to the legs ACAC and BCBC and to the circumcircle of ABC\triangle{ABC}. What is the area of MOI\triangle{MOI}?
<spanclass=latexbold>(A)</span> 5/2<spanclass=latexbold>(B)</span> 11/4<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 13/4<spanclass=latexbold>(E)</span> 7/2<span class='latex-bold'>(A)</span>\ 5/2\qquad<span class='latex-bold'>(B)</span>\ 11/4\qquad<span class='latex-bold'>(C)</span>\ 3\qquad<span class='latex-bold'>(D)</span>\ 13/4\qquad<span class='latex-bold'>(E)</span>\ 7/2