MathDB
Inscribed Circle

Source:

February 7, 2009

Problem Statement

If the three points of contact of a circle inscribed in a triangle are joined, the angles of the resulting triangle: <spanclass=latexbold>(A)</span> are always equal to 60<spanclass=latexbold>(B)</span> are always one obtuse angle and two unequal acute angles<spanclass=latexbold>(C)</span> are always one obtuse angle and two equal acute angles<spanclass=latexbold>(D)</span> are always acute angles<spanclass=latexbold>(E)</span> are always unequal to each other <span class='latex-bold'>(A)</span>\ \text{are always equal to }60^\circ \\ <span class='latex-bold'>(B)</span>\ \text{are always one obtuse angle and two unequal acute angles} \\ <span class='latex-bold'>(C)</span>\ \text{are always one obtuse angle and two equal acute angles} \\ <span class='latex-bold'>(D)</span>\ \text{are always acute angles} \\ <span class='latex-bold'>(E)</span>\ \text{are always unequal to each other}